CHOKES - PAGE 1. Updated pages 2011.
This page 1 is about :-
1. What is a choke? General information about inductance and filter chokes.
2. Measuring choke properties.
Fig1
,  Simple inductance tester.
3. Quick measurement of L.
4. Another quick measure of L.
5. Test CLC filter chokes with DC currents.
Fig 2, Testing choke in CLC filter with DC flow, setting the air gap.
6. Resonance in CLC filters.
Fig 3, curve of LC response.
7. Damping LC resonance.
8. Choke distortions.
9. Chokes for CLC in PSUs.
10. Design method for choke in CLC.
11. Winding method notes.
12. Permeability.
13. Formulas.
14. Other issues CLC.
15. Comparison of CRCRC filters with CLC filters.
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Other related pages :-

For "choke input" power supplies with LC filters and for dc supply to tubes
where a high impedance anode load is desired with high level Vac signals exist
across a choke, go to
Chokes 2
 
For chokes used for dc supply to anodes, cathodes, go to
Chokes 3

1. What is a "Choke"?
I do not know where the word "choke" came from but very soon after electricity was put
to use in hundreds of ways by 1900, people were winding coils of insulated copper wire
around iron to make an inductance to inhibit the flow of ac currents, or to "choke the flow"
of ac, alternating current.

At some point of electronic evolution, an inductance was found to be a good filter device
for reducing noise current flow between point A and B in a circuit. And indeed the right

quantity of inductance and wire resistance
and low amount of stray capacitance may make
an excellent filter element. Whether we use a choke or not depends on the application,
size, weight, cost and perhaps and several other factors.

The unit of inductance is the Henry, named after Joseph Henry, a great American scientist
who died in 1879.

I don't want to get bogged down  into the deep mathematics surrounding all inductors.
Definitions of Inductance are well covered elsewhere on the Internet, and readers need
to read MUCH MORE than I am saying here.

But basically, if there is change in current through a coil of insulated wire there will be a
change of magnetic field produced. This magnetic field change causes production of an
"electro motive force", EMF, which opposes the change in the flow of the current.
This phenomenon is difficult to understand. But if a length of anything which conducts
electrons is brought to be within a changing magnetic field, a voltage across the conductor
is produced which signifies current will flow if the conductor is part of a circuit.
The effect is larger when the conductor is a length of copper wire which has been wound
into a coil. Now if there is no changing outside magnetic field and someone applies a
changing or alternating AC voltage across the coil, there is a changing current flow ie,
alternating current, AC, and a changing magnetic field is immediately created, and this
field tries to prevent the flow of AC current flow causing the field.
It is as if someone unseen is applying some external magnetic field to prevent the current
flow by applying that field to oppose the initial current flow.
There is no outside Interfering Person, but there is magnetism.
The Sun and the Earth have giant magnetic fields and these have great effects on flows of
energetic particles. Magnetism cannot be seen, but we can determine where the
"lines of force" go and what strength of magnetic field may exist. So while not understanding
magnetism at the highest level of university education we can learn how to use it.

A steady unchanging magnetic field may very easily be produced by a coil of wire with
a steady unchanging DC flow of current. This has 101 applications in electro-magnets
used for solenoids and many other applications. In early loudspeakers the anode dc
supply current was fed through a field coil to generate a strong magnetic field within
which a voice coil could work as in an electric motor.

While there is an unchanging
DC flow there is no magnetic field change to oppose
the current change in the coil producing the magnetic field. Therefore the inductor
seems to have a simple resistance equal to the measured resistance of the wire.
But as soon as we change the current, the coil reacts to the change in current to
oppose the flow. So coils of wire have Reactance. This reactance may be quantified
in ohms after calculating Vac applied across coil / Iac flow within coil but the reactance
calculated is only valid for the frequency of the AC. Reactance is proportional
to the frequency of the current flow. This reactance is the "frequency dependent
resistance" and is called the reactance of the inductance, or XL. It should always
be considered as being in series with the wire resistance which must never be
ignored unless it is a very low value. Sometimes the word "impedance" is also
used for an inductor because all "reactances" such as inductors OR capacitors
resistances consist of their pure reactance value dependent on frequency but
in series with their winding wire and lead resistance.

Inductor Reactance, XL, is always expressed as a number of ohms at a certain
frequency.

XL = F x 2 x pye x L, where X is in ohms, 2 x pye = 2 x 22/7 and L = Henrys.

The inductor impedance, ZL, includes more than just pure L, and includes winding
resistance Rw.

ZL = Square root of ( Rw squared + XL squared ) ohms.

If you had a 1.0 Henry inductor of 100 ohms winding resistance, then its ZL at 10Hz
= sq.rt. ( [100 x 100] + [ 62.8 x 62.8 ] ) ohms = 118 ohms.

At 100Hz, the ZL = 635 ohms.
XL = 628 ohms. So you can seen that the winding resistance of 100 ohms does
not just add to the XL of 628 ohms. There is a reason why this is so but I don't have
space to explain it here. But you need to remember this phenomenon. So at high
frequencies the winding resistance makes very little difference to the choke impedance
and for where XL > 10 x winding resistance plus any connected circuit resistance
the winding resistance may be neglected for most circuit calculations.

Suppose we have a simple circuit with AC voltage generator in series with a choke
with a coil of wire wound around an iron core in series with resistance. An equal
value of current will flow through amp, choke, and resistance and 0V ground path.
The magnitude of AC current flow depends on :-

A, The inductance value in Henrys, which can change depending on the properties
of iron.
B, The resistance in Ohms,
C, The magnitude of the voltage source amplitude in Volts.
D, The AC frequency.
E, The presence of steady DC current flow in addition to AC current. The DC current
tends to reduce the inductance value. 

2. Measuring choke properties simply :-
Fig 1
schema inductance test
The Fig1 test set up is shown with an inductance being tested to find its inductance value.
The same test set up could also be used for measuring capacitance values.
This simple test set up requires tools :-
A good signal generator, able to make 2Hz to 200kHz, sine wave, with accurate F indication.
Possible frequency meter if signal gene is poor 
Dual trace analog oscilloscope with bandwidth up to at least 1MHz, with two probes, one for
channel A and B.
Audio amp, able to amplify 7Hz to 25kHz to 12Vrms, so not critical,
AC volt meter with multi ranges and bandwidth of 2Hz to 200kHz and giving Vrms.
Bread board, ie, sheet of ply say 200mm x 200mm with wood screws to which you can solder.
RCA leads, voltmeter leads and amplifier leads.
Solder, patience, persistence, and the will to understand and to never assume anything,
Note book and pencil.
PC and keyboard is NOT NEEDED.
Range of Resistors, 10W wire wound :- 10 ohms, 100ohms, 5W wire wound :- 1k0, 5k0, 10k0.

The most difficult basic thing here is the set up of oscilloscope for balanced mode, aka
differential mode. Learn how to read the oscilloscope manual and how to use what you have,
and if there is no manual, and/or your oscilloscope is single trace, then you have to do some
googling and research because I don't have the time to tell you how to use all the tools.

The signal generator should allow a constant level output voltage to be adjustable for each
of its range of frequencies, and its output resistance should be ideally no higher than 600
ohms so that connection to amplifier inputs does not have any effect on output signal purity
or level. Many "Signal generators" or "Function generators" have "decade" ranges say
2Hz to 20Hz, 20Hz to 200Hz and so on up to 200kHz which an audio tech uses to test audio
gear. The better and more expensive but fragile function generators have a top frequency
of 2MHz, with dc offset, sine wave, square wave, triangular wave, maybe saw tooth wave,
FM and AM modulation etc. But for this test you only need sine waves.

The amp raises the level of generator signal and converts the high output resistance of the
signal generator to a source of signal with a low resistance less than 1 ohm, so that anything
we might connect to the amp will not affect the voltage level at the amp. The resistors used
for testing are placed between amp and whatever L ( or capacitor ) is being measured. 

The points of interest in the above circuit are the measured Vac voltages across the choke
or TP2 to TP3, and across the R or between TP1 to TP2.
The amplifier voltage is measured between TP1 and TP3.
TP3 is always regarded as 0Vac, and a reference voltage.

Suppose we wish to measure inductance of a filter choke, or speaker crossover choke.
Values could be anywhere between 0.1mH and 70H. For this test we need not worry about
DC flow and air gaps because I am trying to get readers to understand basic properties of
inductance. 

Suppose we connect 1k0 resistance between TP1 and TP2 and have an unknown value of
inductance between TP2 and TP3.

For this example, suppose we have a choke with core of 25mm stack x 25mm tongue E&I
laminations, and has  Es butted to Is with a slight but unknown gap between E&I, known as
the "air gap."
The wire size looks to be approximately 0.35mm dia. Let us say we measure the winding
resistance to be 50 ohms which is the same as if the wire was a straight length of unwound
wire. All inductors have some "dc resistance", ie, plain old resistance, and it must be
measured with a dc flow flow only, and R = V / I, which is Ohm's Law.
So all inductances are not perfect reactances and all are equivalent to a resistance-less
inductor plus a series R equal to the measured R. So 50 ohms is effectively in series with
the amount of choke inductance, and in the above circuit is in series with the 1,000 ohms
series R above. Because 50 ohms is 1/20 of the 1,000 ohms its effects on what we want
to measure can be neglected.

A choke may also have some capacitance between layers of windings which sum
to form the "self capacitance" of the winding when measured from one end of the
winding to the other. There is a small amount of capacitance between adjacent turns of
wire and it all adds up among all those turns to be significant. This C will become resonant
at some frequency determined by the formula :-

Fo = 5,035 / Sq.Rt ( L x C ) where Fo is in Hz, 5,035 is constant for all equations
to work,
L is in milli-henrys, C is in uF.

If one were to apply the formula to a power supply filter choke of say 2Henrys with
a typical C = 250pF, then Fo = 7,120 Hz. XC = XL at Fo, so XL = XC = 89k ohms at
7,120Hz. The choke impedance at Fo will be higher than XL or XC could each be at
Fo because the impedance of a parallel tuned circuit is higher than either XL or XC.
The Q of the resonance peak is damped by resistances connected each side of the
choke and by the winding resistance. In general, the choke self capacitance may be
largely ignored for power supply applications but not for where the choke is used as
a load to an anode circuit in an audio amp stage. Nevertheless, the 250pF of typical
choke self capacitance is enough to convey HF switching noise of diodes to the following
audio circuit and if the ESR of the following electrolytic caps is high. The HF diode noise
which appears as little short duration bursts of noise at a 100Hz rate will find its way
to an amplifier output where it may be audible, and I often encounter such noise in my
servicing work. Therefore electrolytic capacitors should have plastic bypass capacitors
across them, 1uF adequately rated is usually enough.

Suppose we set the amp output level to 10.0Vrms, TP1 to TP3.
Suppose we set the frequency to 100 Hz, because we want to know what L the choke
has at about this F. 


Suppose that in Fig 1 above we measure 1.59Vrms across Resistance R, TP1 to RP2.
And suppose we see it is a sine wave on the CRO, (cathode ray oscilloscope), and
distortion is less than 10%.

We can say there is a flow of current, IL, =  1.59V / 1,000 ohms = 0.00159Arms
= 1.59mArms. This flows from amp through L, through R and back to amp via the 0V
rail which consists of ordinary 5 amp rated hook up wire and has resistance less than
0.1 ohms. We also know that there is 10Vrms at the amp output. If we measured the
voltage across the choke we may find it is close to 10Vrms which is measured
between amp output and 0V. We might measure the choke voltage = 9.5Vrms
approximately.

The reactance XL = Voltage across L divided by current flow through L;
impedance follows Ohm's Law.


So XL = 9.5V / 1.59mA = 5,975 ohms.  
XL = L x F x 2 x pye = L x F x 6.28, so L = XL / ( F x 6.28 ),
in this case L = 5,975 / ( 100 x 6.28 ) = 9.5 Henrys.

If we adjust the frequency downwards, leaving the applied amp voltage constant,
we will see that the voltage across choke TP2 to TP3 slowly reduces, and at some
point the measured voltage across 1k0 = measured voltage across choke, and both
will be equal to about 7.0Vac. I can predict that you may find the frequency is about
17Hz. Current in 1k0 = 0.007Amps, and in choke it is the same. Voltage across choke
= 7.0V. The reactance may be found in the same way as before, XL = VL / IL.
7V / 0.007A = 1,000 ohms, and inductance = 1,000 / ( 17Hz x 6.28 ) = 9.5H.
We may find the inductance has become higher at 30Hz than it is at 100Hz.
This is quite common and just because an iron cored inductance measures 9.5H
at one F, it does not mean it will be 9.5H at other F. The iron's permeability ( µ )
changes with frequency as well as with voltage amplitude. An air cored inductor
has a very constant inductance but once there is iron present the inductance
will be much increased over a wide range of LOW frequencies but not in a linear
manner. The non-linearities in a power supply circuit with an iron core may be
ignored, but not where the coke is used for loading an anode circuit.
Usually most E&I laminations have maximum µ at some F below 100Hz, often
around 30Hz. We can measure the choke reactance at any F and/or voltage level
and work out if the choke will suit our purpose. The measurements indicate that
as F is lowered, current flow increases, because XL reduces. Air cored inductors
have a constant inductance all F and all voltages for audio applications but it is
difficult to make large amounts of inductance without using iron cores. An air cored
10H filter choke without iron core and with 50 ohms wire resistance might be
50 times larger than the iron core choke and would be quite an improper and
expensive waste of copper. The choke, and only iron wound chokes have
any uses for audio gear as :-

1, Filter chokes for "capacitor input" CLC  filters in power supplies covered in
this page,
2, Filter chokes for "choke input" or LC filters in power supplies, see Chokes 2.
3, DC supplies or sinks for anode or cathode, known as "choke loading",
or "choke feed", or "para-feed", see Chokes 3.

For filter inductances for speakers, attenuator networks in amplifiers, etc, air cored
chokes are often used because the amount of inductance required is usually much
less than 10H, and air cored chokes become easier and cheaper to make and have
a constant L value and do not generate any distortions. Some modern chokes used
as bass speaker filters to obstruct HF signals have pre-moulded iron dust cores or
a bar made of stacked laminations in a solenoid design to increase L and keep
winding R low. Usually the bar cored solenoid choke raises L by a factor of 4 and
because inductance is about proportional to the number of turns squared, a bar
cored choke can have 1/2 the turns as the air cored inductor of the same size
with the same wire. Chokes in series with midrange drivers or to shunt the LF
signals in HF tweeter crossover filters are invariably air cored.

For filter chokes in power supplies, we really only need to know what the inductance
will be at 100Hz because 100Hz is the frequency of the ripple voltage output from a
rectifier and is twice the mains frequency in UK, Europe, Australia, and elsewhere.
Any power supplies built in "50Hz" countries will work fine where 60Hz mains exists,
such as the USA, although iron wound components designed for 60Hz operation
may not work well when transported to 50Hz countries. I am Australian, and all my
formulas in this site are based around 50Hz mains and metric measurements unless
stated otherwise.

The above test circuit may be used for measuring a whole range of inductance types
for the audio band. The R value may be varied as desired. Practice with measuring and
calculating should train you to work precisely, like the dedicated technician you need
to be to avoid making amplifiers riddled with noise or with a bad smoking habit.

As I said above, Reactance is a name for both L and C circuit elements at a defined
frequency. The pure L or the C reactance actually has NO resistance and therefore
current flow through such reactances does not dissipate any heat, and no work is
done in the L or C. But where the current in reactance also flows in a pure resistance
or tube connected to a reactance, work is done and heating occurs in the resistance
or tube and Power = Vrms x Irms in Watts. It is also equal to
I squared x R, in Watts, or as Vrms across R squared / R, also in Watts.

Electrical energy is transferred by the L or C and can be temporarily stored but not lost
if the L or C is perfect, ie, has low resistance wire or leads. The energy in a choke
becomes stored in its magnetic field; increasing current increases the magnetic field,
and when the current declines the magnetic energy is released. Please search Google
for more extensive explanations about inductance and capacitance properties because
most people remain ignorant of such basic ideas and thus cannot ever learn to properly
design their amplifiers. Once a "hands on" understanding of how L, C and R
behave with AC signals, then other concepts become clear. 
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3. Quick measuring of inductance, using Fig 1 schematic.


The resistance R may be used as shown.

The amplifier level is adjusted for 10.0Vrms.

The voltmeter is held across the R.

The frequency of the signal generator is adjusted until the voltmeter reading = 7.07Vrms.

The frequency where this occurs is recorded.

Now having achieved this, if you measure the voltage across the choke you will find that it
also is 7.07Vrms.
This might be very troubling because your mind will be telling you that if you have 10V
at the amp, and 7V across the choke, there should be 3V across the R, because 10 - 7 = 3.
But your meters are not telling a lie, and it is because of phase shift that the choke
voltage and R voltage when added can be greater than the amplifier input voltage.
If you were to connect TWO oscilloscope channels of a dual trace to view the amplifier
voltage TP1 to TP3, and the choke voltage between TP2 and TP3, then you would find
that the sine wave across L have peaks which are 1/4 of a wave ahead of the amp voltage
peaks. It seems as if the electricity has arrived at a destination before it left the amp.
But it is not so, and relative phase is merely being advanced. If F is reduced, phase
advance or "phase lead" as it is called increases towards a 90 degree maximum.
At some very low F, the XL falls to less than the winding resistance and the XL becomes
a negligible reactance, and the minimum voltage seen is about 0.47Vrms, because 1k0
and Rw of 50 ohms form a resistance divider. You won't be able to measure it because
it occurs at below 0.8Hz, and your gear reads unreliably at that F. Were you to reverse
the positions of L and R, you would see voltage across R fall above say 30Hz as the L
reactance increases. Relative phase between amp and 0V and R and 0V would show
the R voltage peaks behind the amp's, and this is "phase lag".

But wherever you have an R & L or an R & C, there will be a maximum of 90 degrees of
phase lead or lag after attenuation has begun to occur. Where R voltage = L or C voltage,
the phase shift = +/- 45 degrees. This sort of R, L and C behavior needs to be well observed,
and riveted firmly in your brain, if it ever manages to stay turned on properly.

When equal voltages exist across R and choke, then XL = R. From this inductance is
very easily calculated as L in Henrys = R / ( 6.28 x F ).  R in ohms, F in Hz.
When equal voltages exist across R and capacitor, capacitance is easily calculated as
C in uF = 159,000 / ( R x F ). R in ohms and F in Hz.

For example, suppose the choke we were testing above had XL = 1,000 ohms at 14.5Hz,
then the L = 1,000 / ( 6.28 x 14.5 ) = 11H.

Suppose the frequency could not be lowered to enough to get VL = VR, then this
indicates XL is higher than 1,000 ohms. We will need to increase R to some arbitrary
value, say 10,000 ohms, and then if we found VL = VR at 14.5Hz,
L = 10,000 / ( 6.28 x 14.5 ) = 110H, which might be the case for the primary winding
of an output transformer.

We may wish to measure inductance at other frequencies of interest, such as
100Hz for a filter choke.

4. Another quick measuring of inductance with 25k pot,
instead of fixed R in
Fig 1 schematic.

The amp is set up for 10.0Vrms output.

Frequency is set for the frequency of interest.

The potentiometer is adjusted until VR = VL = 7.07Vrms.

The value of R is measured with an ohm meter, or else a 100 ohm fixed R is placed between the
potentiometer and 0V so current in 100 ohms can be measured easily by reading the voltage
across 100 ohms and dividing by 100. The total of resistance of pot + 100 ohms
= ( V pot + 100 ) / current in 100 ohms. One way or another, we can find out the R between
choke and 0V. If measuring the pot resistance we need to disconnect the choke from amp to
prevent measuring the low winding resistance of the choke and to prevent the amp signal
interfering with the voltmeter.

Once we have the R value sorted, L is easily calculated as R / ( 6.28 x 100 ). Suppose we found
R = 5,966 ohms. Then L = 5,966 / ( 6.28 x 100 ) = 9.5H. This agrees with what we found earlier
when we measured the choke to be 9.5H using a fixed resistor of 1,000 ohms.

The frequency where VL = VR = 0.707 x source voltage is known as the LR network "pole" or
"cut off point" or -3dB point. 

The iron cored inductance value changes for applied Vac levels, and during each cycle due to
"hysteresis". The hysteresis causes distortion currents. It is usually of no great importance in filter
chokes. Hysteresis is minimized by an air gap or use of grain oriented silicon steels. This
phenomena should be studied in elsewhere on the Net or in old books.

The saturation behavior of an iron cored filter choke is of very great interest to obtain the
maximum inductance with no saturation for for any choke or transformer winding. A filter choke
in a CLC filter will have considerable dc current flow and usually low AC flow, and the DC flow
will magnetize the iron at some point between zero and the maximum field strength possible in the
iron depending on its properties. The magnetic field intensity is measured in Tesla, and old iron E&I
lams may just manage 1Tesla, while GOSS lams may be magnetized to 1.6 Tesla.

5. Testing chokes for CLC filters with DC current, setting the air gap.
I have sometimes had to supply filter chokes or SE OPTs to people building tube amps and have
set the air gap prior to the sale but without the real amp circuit present.
A simple test circuit may
be made with a low voltage dc current supply as in the Fig 2 schematic.

Fig 2.
schema-choke-test-with-dc-psu-100Hz.GIF

The Fig2 circuit will allow safe measurement of a filter choke using a low voltage
secondary
winding of a 10VA transformer which is easy to find and very cheap.
Providing the DC current and capacitance values are the same as in an amplifier with a
much higher B+, the ripple voltage calculations and filtering action of the CLC will be
exactly the same. The dc current is the same as for a tube amp, in this case 270mAdc.
The ripple voltages at 100Hz will be the same for the tube amp PSU with higher voltages.

R1 is adjusted so Idc = 270mAdc in this case.

Any surplus transformer with winding over 12.6Vrms to 30Vrms may be used in either bridge,
full wave, or doubler config to give Vdc at C1 not higher than +40Vdc.

Setting the air gap in the choke L1.

The choke is shown as 3.3H in Fig 2. This value was used for the example and we only have an
approximate idea of the inductance after winding the choke. The air gap must be adjusted to
maximize the inductance and hence to achieve best filtering with minimum possible ripple voltage
at C2.

The inductance may be calculated for the air gapped value of effective permeability, µe, but as
DC current increases from zero to the wanted working value of µe will be reduced perhaps
50% because of the magnetizing effects of DC current..

To really set the choke to get the best benefit, the choke MUST be tried in Fig 1 test circuit or
in a real amplifier. The gap should be adjusted for size to get the least ripple voltage at C2 of
the CLC filter with the wanted DC idle current flowing.

I place the choke on a block of wood some distance away from the power supply to gain
easy access to the gap between E and I or between halves of a C-core. Once DC flow begins,
The Is tend to be drawn tightly against Es by magnetic forces and there is no need for bolts
to be tight during adjustments.

The gap can be But each time the gap is adjusted, turn off the power and let the B+ discharge.

I have my ac meter and work book set up close by to measure ac voltage across the choke.

I start with no paper in the gap, measure ripple at C2, then place 1, 2, 3, 4, 5, 6 sheets of paper
right across the Es and Is in the gap increasingly, and record the ripple at the second C.
A graph is then easily drawn, horizontal axis = sheets of paper, vertical axis = ripple voltage.
It is important to measure the gap, so that paper may be replaced with polyester
sheeting of the same total thickness as paper.

Paper sheets from the exercise book may be used to establish the gap size because they are a
convenient fine thickness of about 0.07mm. But nobody should ever assume anything,
and the stack of say 120 sheets in note book needs to be measured then divided by 120 to
find the thickness of each sheet. 7mm / 100 sheets = 0.07mm.

One may find minimum Vripple occurs when say 2 sheets of paper installed, with higher
Vripple each side of this null point. I add one sheet of paper extra, and thus for me the gap
has been optimized in case Idc ever increases, as it may, during class AB operation.

When this is achieved, apply some adhesive to all papers, and tighten the clamp bolts making
sure all Is are hard against Es and re-test to make sure Vripple remains low.

If you have no polyester sheeting, you may use paper sheets for permanent air gapping
if you follow these steps.....
After adjusting the gap correctly the choke yoke bolts are drawn up tight to prevent easy
movement or gap increase. Any looseness between bobbin and core should be wedged
with some scrap cardboard, and a layer of cardboard pushed between winding and core
to prevent arcing. The completed choke is then soaked in a vat of polyurethane air cure
furniture varnish for several hours, then excess varnish drained off and the choke allowed
to air dry. The varnish will impregnate the paper and cardboard and then slowly harden
and resist moisture ingress to stop rusting of the iron in the gap which will expand the gap. 

Setting the gap to suit the current to get maximal filtering takes is a much faster way to get
the best from a given choke than by tedious calculations required to do it any other way.
I know of no simulation software available to predict the best gap size.

After the gap size has been established, if the Idc temporarily increases in the case of a
class AB amp, the choke L will reduce slightly and the core might even saturate, but the
slightly increased Vripple will not affect the sound. In well made class AB amps, the Idc
flow rarely increases hugely because the 470uF or more from OPT CT to 0V contains a
huge reserve of energy, like a battery, and transients in music pull all the extra AB energy
from this capacitance. In all the cases of 30 watt AB amps, rarely does the B+ move more
than 1V even with loud passages.

If Idc falls below the rated Idc, Inductance slightly increases, and filtering is improved.

A digital voltmeter, DVM, may be inadequate to measure the ripple voltage below 10mV
accurately because the mains voltage level is constantly changing amplitude because other
people who have many types of equipment powered off the mains will be switching on
and off thus causing switching transients. It is not unusual to find that the signal at C2
jitters up and down with low frequencies with a peak to peak voltage = +/- 0.05V.
Most of the mains LF noise is below 15Hz because the capacitors have become high
value reactances which do not shunt LF signals and choke reactance has become low which
allows LF signals to pass. The LF mains noise does not affect the sound. But to measure
ripple voltage when it is below 15Hz I have shown the RCRCR filter in Fig 2 for reducing
artifacts below 100Hz. The two CR filter sections with C = 0.047uF and R = 100k each
give a pole at 33Hz, and give
about 1dB attenuation at 100Hz, but about 20dB at 10Hz
and 40dB at 2Hz.


An oscilloscope with calibrated mV setting for amplitude is the best way to look at the 100Hz
wave form and determine its amplitude even with some trace movements at lower frequencies.
The wave form of 100Hz ripple should appear without much distortion.
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6.Resonance in CLC filters.

Wherever there is a CLC ripple filter as in Fig 2 above, there will be some series resonant behavior.
In Fig 2, the voltages present include the Vdc rail voltage plus LF noise voltages with F below 100Hz,
and there is the angular wave of 100Hz ripple voltage where there are many harmonics of 100Hz.
In the example shown the ratio of noise and ripple voltage to B+ supply rail is a small fraction and many
manufacturers of tube amps do not bother to filter the B+ rail any further before applying the voltage to
the CT of an OPT in an amplifier. In the past, quite low values of C1 were chosen to suit tube rectifiers
such as in Quad-II where C1 was 16uF and Vripple was about 17Vrms with Ia of 150mAdc. In the
example of Fig 2 or in the 5050 power supply schematic , C1 = 235uF, and Vripple is still significant
at 2.5Vrms for 270mAdc. The higher Idc, the greater becomes Vripple.
For complete prevention of generation of intermodulation artifacts the B+ rail at OPT connection should
be well filtered, especially in the case of SE triode amps. The LC filter is a simple good filtering solution
but the filtering effect reduces as frequency is lowered, and the effects of series resonance should be
prevented.
Fig 3.
graph-LC-response-2011.gif 

Fig 3 shows an equivalent model circuit of a typical CLC filter used to smooth the B+ rail
of an amplifier.

Two possible responses are shown in the graph for 3.3H plus 470uF. Both give about
-56dB attenuation at 100Hz. The L and C form a series resonant circuit at 4Hz.
The reactance of L and C are both each 85 ohms at 4Hz, but together they make
a load which is much lower value at 4Hz.

The voltage generator in Fig 3 shows the mains supply with perhaps only 5 ohms
output resistance at the wall socket.

There is a considerable amount of LF noise and amplitude change in mains supplies.
This means that the LC filter will pass much of the LF mains noise below the LC
cut off frequency to the B+ rail.

Suppose that Source R1 in parallel with reactance of C1 may be a low value less
than say 30 ohms which can be possible in many amp PSUs. Suppose the choke
Rw has very low resistance and R2 is not used. Suppose the amp R3 load is very
high. Suppose the amp is my 5050 where B+ = +515V and Idc draw = 270mA.
This may seem to be load of 1.9k. However, the supply is for 4 x 6550 in UL
mode where the Ra anode resistance for each tube at very low frequencies and with
fixed bias is about 1.3k per per 6550, or about 325r for the 4 output tubes. This
dynamic resistance value is the load R3 on the output of the B+ rail supply. If the
4 tubes were in beam tetrode mode with regulated screen supply each tube's
Ra = 32k, so the total load would be 8k.

Where the R3 "output terminating load resistance" is well above XL1or XC2 at Fo,
and where R1 "input terminating resistance" is well below XL1 or XC2, and where
Rw and R2 is low then any input at Fo will generate high current through the low
impedance undamped resonant circuit formed by L1 and C2, and the resonant peak
shown in the graph will appear in the response. It is possible that the peak in the
response at the filter output at top of C2 may be a higher voltage than that applied
to the input of L1 & C2. The reason for this is that the LC circuit has a high Q at Fo,
ie, any R in series with LC or effectively shunting either L or C is not present,
so there is little "damping."

Fig 3 shows the response of the filter with low R1 and R2 with high R3 for 3.3H
plus 470uF plotted as the "undamped response". If we used an audio amp with
low Rout below 1 ohm with ability to amplify sine waves between 1Hz and 1kHz,
and we had a 3.3H plus 470uF connected in series across the amp output, and
we applied constant level of sine waves between 1Hz and 1kHz, we would see
curve like the undamped response. At 4Hz, there may only be 1Vrms at the input
to LC, but across the C we might measure 5Vrms. The LC filter can produce a
"bouncing B+" rail at Fo, even though it filters the 100Hz ripple so well. To avoid
such effects, we choose low values of C and high values of L to get Fo to be
well below the audio F band.

Consider the situation where a L1 = 5H plus C2 = 16uF for a power amp supply
made in a typical amp in 1955. At 100Hz, XC = 100r, and XL = 3,140r. 100Hz
attenuation is good at 0.032 = -30dB. Fo = 17.8Hz, and much too close to the
audio band. XL = XC = 558r. The pair of 6L6 in beam tetrode used for output
tubes gives a high R load well above XL & XC so the B+ rail would appear to
bounce around considerably at 17.8Hz. Some of this bouncing B+ would appear
at the OPT secondary, and especially if the tubes were configured as SE triodes,
where the triode Ra is low, RL is high, and the B+ rail bounce voltage mainly
exists across the OPT primary load. 

In many amplifier PSUs with CLC filter, the R1 source resistance may quite low
and XC1 may also be low if made a high enough C value. But often we do not
want to make C1 a very high value because we do not want high charge currents
through diodes which help power transformers to be noisy and nor do we want
high inrush currents at turn on. We mainly depend on L1 and C2 for
filtering the B+ rail.

7. Critical Damping of LC filters.

The cut off frequency of the LC filter may be made to be the same F as the resonant
Fo for the LC. First we may assume the R1 resistance with Si diodes plus parallel
XC1 will be a lot less than XL2 or XC2 at their Fo.

There are two places in the Fig 3 circuit where added series resistance is permissible
to "damp" the LC filter response. ( The added resistance acts like shock absorbers
on the suspension of a car to prevent the wheels bouncing at their resonant frequency
with highly undesirable effects. ) L or C Reactance acts like a spring, and just the
right added R reduces resonant behavior so that the peak in the undamped
response disappears leaving the damped response we wish so that low frequency
input signal below Fo from mains are not boosted at Fo at the B+ rail.

The series LC may be damped with R connected across C, or the same amount
of R connected in series with LC.

The two places where R may be added to damp the LC response is at R2 and R3.
The added R need not be any higher than 1.41 x XC2 at the Fo. We have already
established that in most tube amps the tube load will not offer sufficiently low R
close to XC2 at Fo. Therefore there is only one other place, at R2. We will always
wish to keep Rw low to avoid choke heating.

At Fo = 4Hz, with 470uF, XC2 = 85r. 1.41 x XC2 = 120r. Let us say we measure
R1 source to be 25r, and choke Rw is at most 40r to keep the choke from heating
up with the DC flow of 0.27Adc. 
Let us also say the tube load was say 400r.

Damping resistance required = 1.41 x XC.
Added resistance R2 = [ ( 1.41 x XC ) - Rw - R1]  in parallel with R3.

= [ 120r - 40 - 25 ] // 400 = 48 ohms.


We would use 47r, 10W rated. The Vdc drop is 12.7V with 0.27Adc, and Pd = 3.42W.

Whenever R is added between the B+ rail and tubes the regulation of B+ voltage
is reduced. But in most tube amps this is of no concern because with music
signals the audio power is mostly generated by class A action where the Idc
flow remains nearly constant. The added 47r will help to prevent instability at LF.

After connection of the damping resistance into an LC filter, the B+ rail circuit
should be examined with a CRO to measure the reduction of LF noise.
The estimated R2 may need slight increase, or decrease, or to be left out
altogether if there is extremely low CRO trace bounce without the R2.

With a preamp, the tube load is usually a very high ohm load, but Idc is very
low, and if a choke is used the damping R may be increased significantly to
give a response which is overdamped, and a slower rate of increase of
attenuation to the ultimate 12dB/octave possible. In preamps with sufficiently
high HT windings there may be +360Vdc at C1 and only +320Vdc needed
for the anode supplies, and at say 40mAdc flow. Chokes are not needed if
one uses a CRCRC with 3 x 470uF caps and each R = 330r. Each CR
section has a LF pole at 1Hz, and gives attenuation of 100Hz of 40dB.
Two such RC section reduce 100Hz C1 ripple of 0.19Vrms to 0.02mV at C3. 

The filter choke in a CLC supply may be made to be resonant at 100Hz ripple
frequency. This is done by adding a capacitor & series R across the choke.
The R is usually 2 x Rw, and the cap is calculated when the choke inductance
is known. This will have the effect of further reducing 100Hz VR at C2 by a
maximum of approximately -12dB, ie, 1/4 of VR without the added resonant C.
The attenuation of 100Hz harmonics should remain the same but these will be
at a very low level compared to the choke without a 100Hz resonance.
--------------------------------------------------------------------------------------------------------------------

Fo for any LC =         5,035          
                           sq.root ( L x C )
Where Fo is frequency of resonance in Hz, L in millihenrys, C in uF.

Suppose the choke was 1Henry, and C = 470uF,
Fo =         5,035                  
          sq.root ( 1,000 x 470 )
    =  7.3 Hz.

This F is a little high. But to halve Fo, the C must be quadrupled, OR L quadrupled. Or the C
doubled AND L doubled. After seeing how much effort went into the choke and  how large the
choke would need to be if we wanted 4 times the L with 270mA, it may be easier, cheaper,
and just as effective to add three more 470uF caps in parallel with C2, so the C2 = 1,880uF.
However, then the inrush current will be quite high as C1 charges with low wire resistance to C2.
The law of diminishing returns is in operation, because reducing ripple voltage from say
10mV to 2.5mV is usually inaudible. Having 1,880uF to anchor the B+ end of the OPT to 0V
does not do anything better than would a 470uF. Hum in B+ rails when ripple is low could be
from other sources other than an imperfectly filtered B+ supply rail. However, the hum at
the output of my SE 55 Watt monobloc amps with parallel 845 measured only 0.25mV. ------------------------------------------------------------------------------------------------------------------------

8. Choke related distortion with high Vac applied.

The iron cored choke is not easily modeled by an equivalent circuit arrangement. Choke
reactance varies with frequency applied AC voltage amplitude and permeability. During each
wave the choke appear to have less reactance either side of the zero crossing point for the wave.
The value of dynamic inductance will rise until until the core material becomes fully magnetized
and cannot be made to increase its magnetic field. This point is called core saturation. Once the
inductor voltage increases further the reactance becomes zero and the choke acts as a slightly
non linear resistance equal to the winding wire resistance.

This sudden collapse of inductor reactance during wave cycles may be a very undesirable
behavior in most applications wherever we might want to use a choke or transformer winding
and may cause very serious distortions to wave forms or damage to tubes. When the applied
voltage across the choke is reduced during a sine wave cycle the saturation ceases and magnetic
field re-establishes itself and until the voltage amplitude swings to the same value but for the
opposite wave crest so that distortion created is mainly 3H, 5H, 7H etc. The resulting
distortions are not unlike the dreaded crossover distortions in underbiased class AB amps
when the Idc in each PP tube is too low.

Where a choke is used to supply dc to an anode which is CR coupled to a following amp
stage the distortion may be easily reduced to negligible levels by use of resistance in series
between the choke and anode. The tube should always be a low Ra triode and never ever
be a high Ra pentode unless triode connected
. Whenever a very high driving source resistance
is effectively an AC constant current driver source the voltage across a choke or unloaded
transformer primary winding will become distorted by the non linear magnetizing currents
generated in the iron wound coil. The "generator" of such distortion currents within the choke
has a finite impedance value and it is usually lower than the Ra of a pentode but higher than
Ra of a triode. The low Ra of a triode is able to shunt the "distortion generator" within the
choke, so the lower the Ra is, the less iron caused distortion is generated.

Iron wound components when well designed contribute far less distortions to signals than
do the vacuum tubes themselves unless the tubes are beam tetrodes or pentodes without any
NFB applied. The iron caused distortions without NFB can become considerable, as in the
case of the thousands of radio sets made with a 6V6 to power an OPT with no NFB used
anywhere. It is common for many guitar amps with PP output beam tetrodes or pentodes
tubes to have no NFB anywhere thus resulting in high amounts of THD and IMD. The guitar
amp distortions are well tolerated but the awful audio quality from many radio sets was horrid
and permitted only low levels of operation. The quality was made all the worse by the
accountants who ensured quality was minimized in favor of lower production costs and
higher company profits.

For a gapped choke.
The air gapped iron cored choke exhibits a much greater ability to withstand a high AC
voltage being applied without saturation during the wave cycle compared to an un-gapped
choke with the same amount of inductance. This is because the air gapped choke will have
many more turns and a larger Afe to achieve the same inductance of the non gapped choke.
The Bac max does not depend upon permeability, but upon V, Afe, F and No of turns of wire.
So the gapped choke of say 1H will have the same inductance reactance as the un-gapped
choke of 1H, but the gapped choke will sustain a higher AC voltage or sustain the same
voltage but down to a lower frequency without increasing Bmax to saturation. The gapped
choke reactance value is held more constant for the whole wave cycle and for different
frequencies. The air gap reduces the maximum possible inductance to being perhaps 1/20
of the maximum value without a gap because the inductance is proportional to permeability,
and the air gap effectively reduces permeability by artificially increasing the magnetic path
length. So an air gapped choke will need to have much more iron and wire turns to give
the same inductance as an ungapped choke.

In essence, the air gapped choke tends to behave as constant value of inductive reactance
when the frequency is low rather than an higher inductance suffering saturation during
portions of sine wave cycles. In most cases for an air gapped choke or SE transformer
primary there is a steady DC current flow. The air gap much reduces permeability and
therefore reduces DC core saturation, because the core Bdc max is proportional to µ as
well as other things. The presence of the DC Bdc field intensity lowers the maximum
possible AC voltage which may be applied. But the choke or SE OPT allows some
useful function to be achieved with iron and wire when all factors are balanced with
good design and calculations. With DC current present in a choke or OPT primary, any
AC voltage acts to further increase core magnetization or decrease it during each wave cycle.
here is no zero of the ungapped choke with no DC current. Therefore at low AC levels
the choke distortion is low, but generally the gapped choke or SE primary winding
generates even numbered H, mainly 2H.

The saturation effects are due to voltages applied and independent of load currents.

9. Chokes for CLC filtering in power supplies.


A choke in a CLC filter is an effective way to greatly reduce power supply rectifier noise and
mainly 100Hz hum from entering the B+ voltage rail and audio signal path. The aim of using
a choke is to attenuate 100Hz hum by a large factor which justifies the resources spent on
the choke which are greater than if we used an CRCRC filter. A typical use for a choke might
be in a two channel amp where each channel needs 125mA and  it should not have more
than 5mV of ripple voltage at the connections to OPT especially if the amp is a Single Ended
Triode variety with little global NFB and which are far more prone to B+ rail hum than PP
amps which rely on the common mode rejection of noise. SE amps are also all pure class A
so Ia does not change, so good regulation of the B+ supply voltage naturally exists, and the
direct voltage drop across any resistance in the hum filter does not matter if we allow for it
in the choice of power transformer and design the resistance to cope with any heat produced.

The best way to design a filter choke for CLC use is to work from first principles with
Hanna's method clearly spelled out in the Radiotron Designer's Handbook, 4th Ed, 1955,
pages 247 to 250. But I have never found time to convert Hanna's Method to metric units
which were introduced to Australia in the 1960s, so anyone using Hanna's Method will
have to work with inch dimensions.
There is another good little book, 'Coil Design and Construction Manual' B.B. Babani,
first printed 1960, except that it does not delve into air gap setting very well. When I
use Hanna or Babani to check my design for a choke, I simply go back to using Imperial
measures of inches which I still know well.

But not all of you will beg borrow or steal a copy of RDH4, and since most men never
read books any more, I will prod your lazy brains with an alternative and include a typical
example most everyone will find useful at some time if they build any tube amp supply
which needs a supply from 50mAdc to 270mAdc, and for any B+ voltage from +250Vdc
to +550Vdc.

Suppose we want a choke able to take 270mAdc flow, and which will perhaps fit onto a
chassis bolted underneath, and not dissipate more than 4 Watts. Now 4W = I squared x R,
so, R = Pd / I squared = 4W / ( 0.27 x 0.27 ) = 55 ohms wire resistance.

For all copper windings the maximum current density in the wire should not exceed 3A/sq.mm.
You will always find that if you have more than this current density the wound iron cored
article tends to get too hot. In summer, a tube amp chassis gets quite warm so let us not have
hot little chokes, or worse, hot big chokes.

As the core size is increased, the turns and their length increase, so Rw increases, but the
larger size allows a greater area for heat radiation and convection cooling so as long as the
current density is maintained low enough the larger choke with higher Rw won't get much
hotter than a smaller one.

We would need useful amount of  inductance, at least above say 2 Henrys. This is a small
filter choke L value compared to the usual 5H to 10H much favored in 1955. But in 1960,
PSU filter capacitors were very low values of between 4uF and 32uF and everyone put up
with much more noise in amplifiers. Now we would use between 100uF and 470uF without
any hesitation because the modern electrolytic capacitors now made are fabulously reliable
with higher ripple current ratings and designed for continual hard labor in switch mode
power supplies in 1,001 locations including your PC PSU, where 50Hz mains is directly
rectified into a large value C and a 470uF cap rated for 450Vdc costs less than a hamburger.
And the size of the 470uF cap is now not much larger than many 32uF caps of 1955. 
So plenty of C can always be found to complement a 2H choke.

10. Design Method - Choke for CLC PSU.

Nearly all my choke designs start with a choice of GOSS E&I laminated core with 25mm
tongue with 25mm stack. This size of choke can dissipate about 4 Watts of heat without
rising in temperature too much. It will be air gapped, and with an air gap the maximum
µ of the laminations without an air gap need not be high because the gap effectively
reduces the µ to a similar value even if the iron material is GOSS EI lams, GOSS C-cores,
or plain cheap quality high loss non oriented transformer iron with µ max = 2,500 which
often may be found in an old transformer core. So if we know the dc flow, we can
tailor the winding resistance, Rw to suit, and get the best available amount of inductance
filtering. In heavy dc current situations, the Rw needs to be low, eg, for an anode supply
to output tubes, and in low dc current circuits the Rw does not need to be low. In preamps
there is seldom any need for a choke, but a high resistance type with high L value may
be used if available.

So let us accept the simple premise of a 25mm x 25mm core area using wasteless pattern
E&I, and 4 Watts heat dissipation. This will have a winding area available in the bobbin
= 33mm x 9 mm = 300 sq.mm. Turn length, Lt, = 140mm , iron magnetic path length,
ML = 140mm.

A. First question :- "what is the wire size required for the proposed dc current?"

It is mathematically difficult to relate the wanted dc wire resistance, wire copper dia, and
bobbin winding area, and turn number all in the one equation, and it is because of the
enamel thickness involved, which varies in thickness for different wire size, and has a
greater fraction of wire dia when dia is small.

So I have prepared a useful table for everyone to read off the number of turns
required for a given current. The inductance isn't given, because gapping and other
considerations vary widely.

Winding window area = 300sq.mm, average turn length = 140mm, iron magnetic
path length = 140mm.

B. This table allows a simple choice to find wire size for a winding
around a 25mm stack of 25mm tongue E&I.
 

Cu wire dia, mm
turns, max.
Resistance, ohms
DC current max
 L, Henrys
µe = 200        
0.20
4,800
380
89mA
25.0
0.25
3,100
157
138mA
10.8
0.30
2,200
77
197mA
5.4
0.35
1,600
42
267mA
2.88
0.40
1,300
26
339mA
1.9
0.45
1,050
17
420mA
1.24
0.50
870
11
522mA
0.85
0.60
600
5.3
752mA
0.40
0.75
390
2.2
1.16A
0.17
1.00
230
0.73
2.02A
0.06
1.40
120
0.19
4.0A
0.016
2.00
60
0.05
7.7A
0.004

The wire current density is all slightly under 3A per sq.mm for all wire sizes.
If current = 270mA dc, simply choose the wire size for the current rating just above
270mA, ie, 339mA and the wire Copper dia = 0.40mm, and you should get 1,300
turns onto the bobbin. Or put another way, if we had a spool of 0.40 wire, we
know we could have 1,300turns and with 330mA. 

The table does not show that if the stack of laminations is increased, the inductance
increases in direct proportion, so that if stack was 50mm, then L would double
with the same current. Winding turn length and Rw also increases so heat losses
also increase, but because the surface area increases, the temperature should
not increase.

C. I did come up with some useful formulas....

For where N and Lt and d is known...

Winding resistance, Rw   =    N x Lt x 0.0000226     for all core sizes.
                                                   d squared
where Rw is in ohms,
N is turns,
Lt is turn length in mm,
0.0000226 is a constant for all equations and because the resistance in ohms of
1 metre of 1mm dia wire = 0.0226 ohms, and d is the copper dia of the wire we are
using in mm.

From the last equation, and for a 25mm stack of 25mm tongue size,

Rw = 1300 x 140 x 0.0000226 / 0.4 x 0.4 = 25.7 ohms.

D. Here is a formula for a core with equal stack and tongue size T to be
found
for a given wire size and wanted winding resistance...

T = 25 x cube root of Rw x cube root of ( d squared  x od squared ),

where 25 is a constant,
Rw = ohms,
d = Cu dia of wire,
od = overall wire dia including enamel.
 
So for 26 ohms and d = 0.4mm, and od = 0.47mm,

T = 25 x 2.92 x 0.328 = 23.94, and we would choose 25mm.

If the resistance was to be 50 ohms, with the same wire size,

T could be 25 x 3.68 x 0.328 = 30.2, so we could choose T = 32mm.

Then actual number of turns can easily be worked out once a core window size
becomes known from the T dimension and a wire size has been chosen has been
chosen. The winding window area size = length of window x height of window
= 1.5T x 0.5T = 0.75T squared for wasteless pattern E&I lams. For T = 25mm,
Area window = 468 sq.mm. But allowances for the bobbin cheeks and bobbin base
and for final winding clearance from iron all equal to approximately 1.7 mm all
around reduce winding area to 34.1mm x 9.1mm =  310sq.mm, or 0.5 x T squared.

E. Calculating turns N.
The copper wire dia may 0.4mm, but the overall diameter of class 2 high temp
rated polyester-imide enameled magnet winding wire will be 0.47mm, and thus
possible turns are :-

N = Bobbin Window area / oa wire dia squared = 0.5 x ( T/ oa wire dia ).

If we have wire = 0.4Cu dia, then oa dia = 0.47mm.
If we choose T = 25mm, then N = 0.5 x ( 25/0.47 )squared = 1,414 turns which
is close to what is conservatively estimated in the table above.

Should anyone wish to use a larger stack of 25mm laminations, then the turn
length will increase from the 140mm used to make the table, and winding resistance
will increase, but as I mentioned, this is of little concern if the current density
remains constant.

Let T = S = 32mm.
If wire is 0.47mm oa, N = 2,317 approx and inductance will be much increased,
all other things being equal. The same inductance may need a stack S of 75mm
with T = 25mm if N is only 1,400t. For most E&I cores, the stack should not exceed
3 x tongue width. The higher the stack, the more difficult it becomes to clamp all
Is tight against the Es, and a special clamp must be arranged.

11. Winding.
Neat layer winding methods are best where patience, skill, and machine lathes allow.
These days polyester-imide coated high temp grade 2 winding wire is much more
rugged than fragile enamels of the past and wire can be wound on without layering
neatly, but gradually letting turns pile up while slowly feeding on wire while *slowly*
traversing the wire across between cheeks to avoid wire crossings at a wide angle,
and and thus preventing a small wire to wire pressure area which could lead to a
short circuit between one point in the winding and another. Such shorts prevent
any inductance being maintained. The level of the wire should be kept free as
possible from forming large humps and troughs while traversing the bobbin
especially when you get close to nearly filling the bobbin. Skill and practice gets
it right. Tension in the wire is light, and varnishing can be done as you go with
Wattyl 7008 floor varnish daubed on after each 200 turns. This terrible smelling
and possibly toxic varnish has a pot life of hours before setting to become a
rugged hard polyurethane which promotes heat transfer from inner winding layers.
Once winding is complete, some insulation tape should be wound twice over the
top of windings for basic protection and the maximum height checked to ensure
it can later fit into the bobbin hole without touching the iron anywhere, thus allowing
another layer of 0.2mm polyester sheet to be slid between iron and winding to
ensure arcing cannot occur between iron and coil wire. Terminations on the bobbin
should be provided where wire is less than 0.75mm dia.

Some of you may have the book, Coil Design and Construction Manual B.B. Babani,
first printed 1960 and re-printed 14 times I know of. Mine is a 1991 copy, somewhat
grubby from from so much use.

Some people will just try to read the tables in the book and wind something,
and maybe they end up with a sub optimum choke that lacks enough inductance
which is all too easy to do especially in the case of a choke for a choke input power
supply. Babani's book with its tables requires someone to have lots of experience
and an IQ = 259 to be assured of not making a mistake. Neither exists in the
minds of many DIYers.

People may find some old and useless transformer with an open winding which
may yield a suitable amount of iron for a choke. Chokes in PSU do not demand
that the iron be top grade GOSS. I have obtained material from re-cycled cores
often. First you remove any bell ends, yokes and bolts if possible for re-use.
To extract E&I laminations from a well varnished transformer is difficult because
they are all glued together by varnish. If you simply place the transformer into
a small wood fire for 20 minutes and heat iron until just cherry red hot, the heat
vaporizes and burns off any plastics. Next day when the lams have cooled, the
E&I lams will all just fall out loose, and the heat will have annealed the iron and
won't affect the iron's magnetic qualities.

Unfortunately many people won't be able to light a fire anywhere to fry old chokes
and transformers and the smoke is toxic, although the heath hazard produced by
DIY people doing dirty filthy craftwork processes is infinitesimal compared to what
mainstream industries are doing 24/7. But once the old iron is cooked and had
cooled the copper turns will be free of insulation and bobbin and may easily be
cut loose and removed to a re-cycling bin. Don't cool the hot cores in water.
Don't try to clean the oxide layer off the laminations, it insulates the iron laminations
from each other which prevents eddy current losses.

If the material is not 25mm tongue size, the turns and current and wire size will
have to be worked out to suit the window size.

12. Permeability.
At this point I must discuss the iron permeability known as µ because for all
the chokes we make, it will be varied to suit the purpose of the choke which
usually means the iron will all be placed into the bobbin in a few basically different
ways apart from method A below, each method has the effect of effectively
lengthening the magnetic circuit length, and thus reducing the maximum possible
permeability, µ, to effective permeability, µe.

(A)   All Es and Is are reversed in direction as they are stacked up, and E&I are thus
maximally overlapped and interleaved. This gives the choke the maximum inductance
it can ever attain with NO DC present because µ will be at a maximum and for high
grade GOSS material it can be 17,000. This method is usually only ever used where
no dc flow is present.

(B)   All Es are piled together facing the same direction as they are stacked and a
pile of Is clamped to the pile of Es with polyester sheet gapping material inserted when
we know what size to use. Even without any gap and Is are hard against Es, the
maximum µ available will probably be approximately 1/10 of the value it was when
maximal interleaving above was used in (A). The resulting µe for anything other than
maximal interleaving is the effective µ, known as µe. This is because the core has
imperfect mating surfaces, and the change of grain direction between all E and all I
has the effect of an equivalent gap larger than what is actually physically present.
So the maximum µe for a butted core without a gap can only be measured if we
need to know what it is. It cannot be accurately calculated.

(C)  Es for the whole choke are divided into into say 5 piles of equal height. Is for the
whole choke are divided into 5 piles of equal height also equal to piles of Es. A pile
of Es is inserted to through the bobbin hole, and a pile of Is are butted to the pile of Es.
Then another pile of Es is inserted in the opposite direction and another pile of Is
placed to close this pile of Es. The process of alternately directioned piles of Es and Is
continues until all Es and Is have been assembled. Tightening of the finished stacks
may be done with some additional Es and Is placed on the top and bottom piles.
When bolted partially tight with holding yokes the Es and Is may be tapped up close.
This method allows the µe to be intermediate between being maximal with maximal
interleaving and the µ/10 value or less achieved above in (B). This method is rarely
ever used, but applied sometimes to PP OPT or in a balanced choke with a CT on
the winding where one wants the core to resist being saturated by unbalanced DC
currents in each 1/2 primary, and still be able to get a high enough and more constant
amount of inductance, with freedom from saturation.

For all amplifier power supply filter chokes, there will ALWAYS be a full gap between
all Es and Is and ONLY method (B) is ever used.

When E&I are stacked close, maximum inductance without a dc flow can be determined
with the test shown on the top of this page where we apply a signal at 100Hz at about
10Vrms and measure current in a sensing resistance, and work out the ZL at 100Hz.
Then the inductance is calculated from L = ZL / 628.

13. Formulas, µe, air gap, Bdc, Bac.

A.    For all choke inductances, L  = 1.26 x Nsquared x Afe x µe
                                                                 1,000,000,000 x ML

where L is in Henrys,
1.26 and 1,000,000,000 are constant for all equations,
N is the turns,
Afe is the cross sectional area of the core in sq.mm,
and µe is the effective permeability,
and ML is the iron path length.

So µe   =   1,000,000,000 x ML x L  
                    1.26 x Nsquared x Afe.

Let us suppose the maximum L of the example inductance with 1,300t on
Afe = 625s.mm with a close butted core = 3H, and with no dc present.

µe max   =    1,000,000,000 x 140 x 3  
                   1.26 x 1,300 x 1,300 x 625

              =     315.

If the µe was reduced by the presence of dc or by placing a gap into the core
with sheets of paper so µe = 200, L would become 1.9H.

NOTE  Adding a gap of 1 sheet of 0.07mm notebook paper for a gap
right across the core gives a total REAL gap of 0.14mm ! ! ! !

This is because in an E&I core there are TWO gaps in ONE magnetic length,
one each side of the holes bounded by E legs and I.

Major errors in gap length calculations and choke function can arise if this
fact is not remembered carefully.

B. So adding a gap.

Add gap = 0.14mm will change µe.
µe   =          µe max of iron butted close without a real gap                 
                   1 + ( µ max  x gap in mm / ML of iron in mm )

Suppose in this case µe =              315                  
                                           1+ ( 315 x 0.14 / 140 )
                         =   315 / 1.315
                         =  239

C. DC field strength Bdc.

What is the magnetic field strength Bdc when we have 270mA,
core = 25 x 25, and  µe = 239?

The dc field strength for a choke, Bdc = 12.6 x µe x N  x Idc

                                                                        ML x 10,000
where Bdc is in Tesla, ue is effective permeability,
N is the turns,
Idc in Amps dc,
ML is the magnetic path length of the iron in mm,
and 12.6 and 10,000 are constants for all equations to work.

In this case Bdc = 12.6 x 239 x 1,300 x 0.27 
                                   140 x 10,000
                         =  0.755Tesla

This means that the iron is magnetized by the dc current to a large portion
of its full capability. If the iron is GOSS, it may saturate at 1.5Tesla,
and if it is old low grade iron maybe at 1Tesla.

Maximum Bdc should not exceed about 1Tesla for CLC chokes.

We also need to keep in mind the AC field strength, Bac, and and keep the total
of Bdc + Bac to below 1.2Tesla.
In the case of the CLC filter we have, the Vac across the choke is only 1.2Vrms.

D.  AC field strength, Bac.

The AC field strength, Bac   =   22.6 x Vrms x 10,000
                                                          Afe x  N x  F
where 22.6 and 10,000 = constants, Vrms = voltage across the coil,
Afe = core section area, N = turns, F = frequency in Hz.
In this case, Bac = 22.6 x 1.2 x 10,000
                            625 x 1,300 x 100 
                         =  0.0033 Tesla,
This Bac is quite insignificant, and may be ignored as it will make little difference to the
sum of Bdc and Bac.

How well will this choke work with dc flow in a real circuit?

The CLC choke performance depends heavily on the gap size, which is adjusted as
I have said above.

14. There are other issues to address with a CLC filter...
At turn on in a tube amp with CLC supply, C1 and C2 require charging up to full working
voltage, say +420Vdc, and the total C could be 5 x 470uF = 2,350 uF. The flow of current
in the first few mains cycles at turn on during charge up is quite high. There is also
magnetization current of the mains transformer, and the current is only limited by the
mains wiring resistance, series resistances of windings, and diode resistance and
winding resistance of the choke. The high charge current can cause a mains fuse
or any secondary fuse we may have in the HT winding to blow all too easily.
And even when all is charged up, and the amp is working there will be quite high
peak charge currents of perhaps 1.3A peak flowing into C1. Where a voltage doubler
is used, the peak charge currents at the HT winding will be twice those at a full wave
winding, maybe 2.6A.

It is good practice to arrange a resistance in series with the mains
of say 100 ohms
with 20 Watt rating
which causes a delay of B+ rise to 2/3 its final working value after
4 seconds. After 4 seconds a relay shunts the 100 ohms and B+ continues to rise to a
peak value. This will much reduce and limit "inrush" charge currents and initial filament
currents. Further reductions in peak charge currents into C1 is possible using permanent
series R between Si diodes and C1, where R may be approximately 7 x XC, so that
if C1 was 470uF, then XC = 3.4 and R = or 22 ohms, 10W rated. The effect of the
22ohms increases the time it takes to charge C1, and the saw tooth Vripple wave form
will show charge time for caps lasting nearly as long as the discharge time when DC
flows to the amp. The Vripple measurement does not change with or without the
22 ohms. Ripple current = Vripple / XC, which always works out to 1.41 x Idc.
If Idc = 0.27A, then Ir = 0.38A rms, and with C1 470u, Vr = Ir x XC = .38 x 3.4 = 1.3Vrms.
But the wave is not a true sine wave, but result is close enough. Peak current
cannot be less than 1.41 x 2 x 0.27A, say 0.76A because during cap charging the diodes
must have to charge the cap plus supply the amp current. Its not unusual that maximum
peak charge currents when C1 becomes a huge value is 6 x Idc, or 1.62A, and only
limited by transformer and diode resistances. By a huge value, it is when the time
taken for caps to charge = about 1/6 of the total cycle time for charge and discharge.
Although the CRO sees the saw tooth wave as an innocent looking wave form the current
wave form is a very different picture. Basically, you simply want the cap charge time to
be just less than half the total charge and discharge time so to work out the series R,
inspect the wave form and add the R to give you the near equal times. This added R
usually reduces transformer noise and reduces heat in the HT winding. The heat in the
series R will be considerable, and more than if you try to calculate Heat = V squared / R.

If a CT winding is used, the 22 ohms can be placed between CT and 0V, or 22 ohms at
each end of the winding to diodes. If a doubler is used, one would have two 22 ohms
in parallel for 11 ohms in series with the one doubler winding.

If you measure the performance of the B+ power supply with added R to reduce peak
charge currents, you will see these resistors cause slight de-regulation of the B+, but
as I have said elsewhere it is not important because all your music is made while the
tubes are in class A and there is very little change in current from the power supply,
so very little B+ voltage rail change.
The +Vdc will also be slightly lower than the possible maximum at C1. If instead of +440Vdc
at 270mA, you get only +430Vdc with limiting resistors, its OK, because the power
transformer will run a little cooler, and instead of dissipating so much heat in the HT winding
with such high charge currents, the peak currents are lower, and heat is mainly in the limiting
resistors. If the fuses don't blow during a fault, or protection circuits fail, you want some
cheap resistors to fuse open rather than have a destroyed output transformer or power
transformer. 

Peak charge current can be limited further by using a lower value for C1, retaining such
resistances, and placing more C after the choke.

Tube rectifiers of any kind will destroy themselves if the capacitance values exceed allowable
values given for the wanted Idc given in the data sheets. So for 270mA dc and 440Vdc, and a
full wave CT winding, one may have TWO GZ34, one on each phase of the winding.
C1 = 100uF would be the safe value, and ripple voltage will be much higher, at about 6Vrms.
The reactance of 100uF at 100Hz = 16 ohms, and if there is 6Vrms at 100uF, ripple current =
375mA, which is about 1.41 x 270mA. The natural "on" resistance of the GZ34 is the anode
resistance of the diode tube, and is high, and which limits peak charge, so added resistances
have to be high to achieve any peak I reductions. In fact with tube rectifiers, the Vac to Vdc
ratio is often a low 1.2:1 or lower loaded, but with Si diodes it about 1.35:1 loaded. Tube
rectifiers get hot because average voltage x average current = large waste of heat.
Sometimes I have rugged polyester motor start capacitors for C1, and sometimes because
I have a transformer that has a HT winding with a very high Vac and no taps for adjustment.
In 2009, I made two 60Watt SE monoblocs each needing +480Vdc at 330mAdc, so 660mA
total from one large power supply chassis. HT winding gave 420Vrms giving a maximum no
load Vdc = 590Vdc, and working Vdc of +560Vdc if C1 was a high value, so somehow
I had to drop from +560Vdc to +480Vdc which is 80Vdc at 0.66A, and power wasted
= 53 Watts, which I didn't want to waste. I used C1 = 30uF using 2 x 60uF in series,
each rated for 400Vdc and Vripple was very high, but charge currents low, and no heat
is liberated because of AC in a reactive C or L component, so I got the +480Vdc I wanted.
C1 was followed by a 4Kg choke of about 10H, and then by 4 x 470uF series /parallel for 470uF
total and Vripple was less than 35mV at C2. I had an RC filter following that with R = 50ohms
and C = 705 uF and Vripple < 2mV. The added second RC filter damped the resonance in first
CLC filter at about 3Hz.

If you have a pair of tube rectifiers to feed 100uF and then have choke plus an enormous
following C value, during charge up the tube rectifier really struggles, and can experience
excessive peak currents causing internal arcing inside the tube. Too many arcing occasions
hasten the death of the tube rectifier. Such GZ34 might be OK in a Quad 22 with pathetically
low value C and almost non existent B+ rail filtering before the CT of OPT. Tube rectifiers just
do not belong in modern amps with large amounts of C, and I never use them.

The filter choke in a CLC supply may be made to be resonant at 100Hz ripple frequency.
This is done by adding a 400V rated polyester capacitor plus series R across the choke.
The R is usually 2 x Rw, and the cap is calculated when the choke inductance is known.
This will have the effect of further reducing 100Hz VR at C2 by a maximum of approximately
-12dB, ie, 1/4 of VR without the added resonant C. The attenuation of 100Hz harmonics
should remain the same but these will be at a lower level compared to the choke without
a 100Hz resonance.
Using a 4H choke with Rw = 30 ohms can be made partially resonant
at 100Hz with C = 0.63uF and R = 68 ohms, 5W.  


15. Compare CRCRC filter to CLC filter.

Let us first consider the power supply with diodes charging a C of 470uF then with TWO
following RC filter sections, with all C = 470uF and each R = 50 ohms, using 2 x 100r x 10W.
Let us suppose Idc = 270mA, and total R in a CRCRC = 100 ohms, and there would be
13.5 Vdc across each 50 ohms. Heat generated in all R = 0.27 x 0.27 x 100 = 7.3 Watts
with 3.64 W in each 50 ohms. To escape damage during faults or overloads, each 50 ohms
is rated for 20 Watts and perhaps mounted on a heatsink if chassis space allows, glued
with a bed of hi-temperature silicone sealant 'Selleys 401'. Or we might use a pair of
aluminium clad wire wound 47 ohm resistors bolted with heat paste to the chassis or a
heatsink, or we might use Welwyn vitreous enameled resistors slung between turrets
and hanging in the passing air flow above vent holes in the chassis bottom plate.

With 270mA, C1 of 470uF will have ripple voltage = 1.3Vrms at 100Hz. The following pair
of R&C filters using 50 ohms plus 470uF will each have an attenuation factor = XC / R
= 3.4 / 50 = 0.068. Two cascaded filter section have an attenuation factor = 0.068 x 0.068
= 0.0046 so ripple voltage at the output of C3 = 1.3V x 0.0046 = 0.006 Vrms, ie, 6mVrms.

This could sound a little over zealous, and for an RC filter with even lower heat losses in
resistances, the R value could have a minimum of 10 x XC, or about 33 ohms. Thus an
overall attenuation factor at 100Hz of 0.01 is available to give Vr = 13mVrms. Three
such RC sections after C1 will give attenuation factor = 0.001 and Vr = 1.2mVrms.
Total R for 3 RC filter sections with R = 33 ohms each will perform better than 2 RC
sections with total R = 100r. There are no resonance effects to worry about.

let us suppose we wished to match the performance of a CRCRCRC filter with a CLC filter.

Let us assume we have C1 = C2 = 470uF. For an attenuation factor of 0.001, we
must have XL = 1,000 x XC at 100Hz. With each C = 470uF, XL = 3,400 ohms.

The inductance required = XL / (6.28 x F) = 3,400 / 628 = 5.4Henrys.

The winding resistance may easily be made less than 100 ohms, but may be 50r, so
the choke would have Pd = 3.65 watts, The frequency resonance, Fo, between L and the
C2 must be checked. Fo  = 5,035 / sq.root ( L x C ), = 5,035 / s.rt ( 5,400 x 470 )
= 3.16Hz. This is below 4Hz and acceptable for any PP or SE amplifier.
At 3.2 Hz, XC = XL = 106r and to obtain a low Q for the resonance peak the series R
between L and C2 should be under 106 ohms. If we used a 50r added resistance to
the Rw of 50r we would have good damping of the LC resonance Q.

To make the LC equal the performance of resistors in every way including a cure for
resonance the series resistance of both CLC filter and CRCRC will be about the same. 

If we were happy with Vr being say 4 times higher at 4.8 mVrms, the choke value could be
quartered to 1.35H. But then with C2 = 470uF, Fo increases to 6.3Hz and it is getting too
close to the audio band. The damping of the resonance Q would require some additional
series resistance. However, if 1.35H was all we could afford, we might double C2 value
to 940uF and achieve Fo = 4.4Hz, probably acceptable, while reducing Vr to 2.4mVrms.
A 1.5H choke would be fine and much easier to make than a 5.4H choke.

In the case of where the available electrolytic caps have ratings of 450Vdc working
and B+ = +420Vdc working and peak with no load at less than +450Vdc, all is well.
But where B+ exceeds +430Vdc when loaded it is safer to use seriesed electrolytic
caps each rated for +350Vdc working. The C1 = C2 = 235uF, and we would want L
to be at least 5.4H so that Fo = 4.5Hz, barely acceptable. Vr would be 4.8mV at C2.
Added R for suppressing resonance would be about 100r.

For CRCRCRC with each R = 68r, total for 204r total to get a final Vr attenuation
factor of 0.001. Heat Pd = 15 Watts.

Both CLC and CRCRCRC will dissipate heat in resistance, although the choke plus
R will total about 150r so heat = 11 Watts.

If our resources allow us to easily make a choke, or we have bought one cheaply,
or find a suitable type in a pile of junk, we should use that choke. But to improve an
old amp, or for where little spare space is available for a choke, then RC filtering
with high cap values is easier.

If someone you know is just plain infatuated with chokes, well OK, leave them to
their choking experience. If you don't like chokes, then use bagfulls of capacitors
to minimize series resistance values. A 470uF x 350V rated electro is about $7.00,
and about 1/2 the price of a McDonald's large hamburger that may make you feel fat,
sick, and worse than had you bought a capacitor. But a 5.4H choke might cost the
same as 7 hamburgers. People argue about costs of audio gear parts. But I don't
know why they spend so much on garbage food and 101 meaningless other things.

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