Frequency Response Testing of amplifiers, February 2013.

During construction of any amplifier, there is always a need to plot the frequency response graph

and to examine the stability with transient input signals.

What is always wanted is that all power amplifiers have a flat frequency response between at least

20Hz to 30kHz with no more than -1dB attenuation across this range, and we wish that the response
below or above this range has no peaks exceeding +3dB, regardless of the load which may be any
possible pure resistance, or with any possible combination of R plus inductance L or capacitance C.
All amplifiers must be able to remain unconditionally stable ( free of any oscillations ) even without any
load connected at all.

To achieve the response and stability required, we need to have suitable test equipment including the

following items :-

1, Sine wave signal source from 2Hz to 200kHz with THD < 0.5%, with up to 3Vrms amplitude.

2, Square wave signal source for at least 4 frequencies between 100Hz to 500kHz, and preferably
with 12 frequencies, and 3 F per decade and with rise time of at least 50V/uS.
3, Wide bandwidth Vac volt meters for measuring of large voltages between 1Vrms and 500Vrms,
with medium accuracy for F between 2Hz and 2MHz.
4, Wide bandwidth Vac volt meters for measuring voltages between 1mVrms and 1,000Vrms
between F 2Hz to 2MHz with high accuracy.
I have several analog Vac meters for measuring anode voltages and other high level signals over a wide range
of F.
I do have several digital meters which are accurate for Vac up to only 1kHz.
5, Radio variable 2 gang tuning capacitor giving C between 50pF and 800pF,
and combined with good quality 25k linear potentiometer in series to make a Zobel network
that can have its R and C varied while observations are made with oscilloscope and with square wave
input.
6, Analog old style oscilloscope ( aka Cathode Ray Oscilloscope, CRO ), with 2Hz to 2MHz bandwidth.
Preferably a dual trace unit capable of DC to 15MHz is used.
7, A variable dummy resistance load capable of full power testing for several minutes. R load values should
be selectable between 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16 ohms, and possibly more ohms up to 32 ohms
by adding yet more series connected high wattage R.
8, Capacitor loads need only be rated to take the expected amplifier voltages. They normally do not heat
up when subjected to considerable signal voltage, but the amplifier will heat up due to current flow.
9. Power amp speaker cables with low resistance. 15 amp rated mains cabling is fine, with 4mm banana plugs
each end to connect from amp to dummy loads fitted with 4mm banana sockets.
10, Interconnect RCA cabling of normal high C of say 100pF and 1 metre long plus others of 500mm long
with less than 20pF.

What makes a useful sine wave and square wave generator? Usually, many people use what is called a

function generator which puts out sine waves, square waves, triangular waves and has such extra abilities as
AM and FM and variable square wave intervals between even spaced +/- waves peaks, and has DC offset
adjustment. In fact, only sine and square waves are needed. Low distortion in sine waves is not critically
important for response measuring as it is when measuring THD, so anything with THD < 0.5% is OK.
Square waves need only a rise time of 50V/uS with no benefits of having say 500V/uS.
Signal generators should have maximum output resistance of 600 ohms to ensure the input resistance of amplifiers
has little effect on the output level of the signal generator.
I am presently using a sine/square gene with 1.8k potentiometer at its output which means its maximum approximate
Rout = 600 ohms and surprisingly, with a normal high capacitance RCA cabling to my CRO, there is considerable
reduction of rise time of square waves. But at least all F up to 500kHz are unattenuated from the gene.
Better signal genies have Rout = 50 ohms, which means the gene would need to have a a buffered output using a
pair of complementary npn and pnp source follower mosfets after the attenuator pot inside the sig gene.

But unless otherwise stated, assume all measurements are done with sig gene of Rout < 600 ohms.


To make a graph of F response between say 1Hz and 1MHz, one can use the oscilloscope ( CRO ) as a volt meter.
Suppose you have a 32Watt amp which makes a maximum Vo = 16.0Vrms into 8r0. The response with a pure
8r0 load can be examined with the amp running at 16Vrms at 1kHz and the trace on the CRO is set so peak
to peak waves occupy 1/2 the screen height, and centered. If the Vo increases by +6dB the sine wave will occupy
the whole screen height, and if -6dB it occupies 1/4 of the screen height. This method will show small Vo changes
of only +/-1dB, when Vo will be 1.12 x 16Vrms or 0.89 x 16Vrms. A scale drawn on masking tape may be put
on each side of the screen to offer logarithmic calibration so you know levels of +/-3dB, +/-6dB, -9dB, -12dB.
Practice with the CRO stops your confusion. The CRO should have 10MHz BW, and for best LF Vo measurement,
always use the DC option on switch for DC or AC.
The amp secondary winding on OPT should have one end taken to 0V.

To record your measured response with sine waves at the frequencies produced by oscillators below, you can
make a printed paper copy of a response sheet then plot Vo levels with a pencil. Clever Dicks among you
will use a PC program but usually they are limited to 20Hz to 20kHz, and you NEED to measure a much wider
response.

Here is a sample response sheet which you may copy....
Graph 1.
graph-F-response-dB-5Hz-320kHz-5x5mm.GIF 
This may be extended at left side down to 1Hz or raised on right side to 1Mhz, and I leave YOU to decide
how big you want it to be a printed A4 page. Once you get the page you want, many copies can be made.
I spent many hours getting the logarithmic scales just right as I could. One sig gene I have has same switched
F output as the vertically written numbers 4.7, 5.6, etc, The spacing is even along the logarithmic scale.
Once a row of dots have been penned on the graph sheet, just join the dots with a smooth curve where
response changes, and you have a very good idea of the response.
Measuring the response can tell you all about your mistakes. It is hard disciplined work to properly measure
an amplifier.
Response levels should be measured at 0dB, which would be 16Vrms for a 32Watt amp with 8r0 load,
and then at -6dB = 8Vrms and at -12dB = 4Vrms. The best indication of stability and HF and LF behaviour
and especially with pure C loads between 0.1uF and 2uF is done at the -12dB level where it will be safe
to test up to 100kHz with 2uF connected, and where this 2uF has Z = 0.8r, which is nearly a short circuit.
Don't test at 0dB with 2uF.
Don't leave the amp running for long at high Po when testing below 20Hz and there is distortion caused by OPT
core saturation. The response you wish to understand is that where THD < 2%, which you can see on the CRO
as sudden appearance of very distorted waves due to core saturation at LF, or appearance of triangular waves
at HF known as slew rate distortion, ie, some stage in the amp becomes overloaded at HF.
Therefore you may find the response for Vo = 0dB may have -3dB poles at F1 = 20Hz, F2 = 40kHz.
But at Vo = -6dB, F1 = 12Hz, F2 = 80kHz, and at Vo = -12dB, F1 = 5Hz, F2 = 60kHz.
There will always be peaks in the response at LF if the open loop phase shift is high and you have not used
LF gain shelving. Similarly, peaked response occurs with a pure C load usually above 15kHz. and to minimize
the peaking there must be zobel networks applied carefully within the amp.
The idea is to get the widest 0dB response with a pure R load which is the correct load for the amp,
yet not have peaking any more than +3dB at any F regardless of pure C load use.
The response with zero load at all should not be measured above the 0dB Vo reference level for the R load.
It can be measured at any level below 0dB. The amp open loop gain is highest when there is no load connected.
While there may be say 16dB GNFB connected when an 8r0 load is used, this amount of GNFB depends on the
open loop gain, ie, Vo divided by Vin without any GNFB connected.
Without any load, many tube amps oscillate at LF because their open loop gain of the output tubes has perhaps
doubled which increases the amount of GNFB applied which may make the amp work at a level above the
"margin of stability". This margin of stability is expressed in dB, and it means the amp becomes unstable if
the amount of NFB is increased from the safe level by a certain number of dB. In a real amp with 16dB of GNFB,
it may begin to oscillate if GNFB is increased by say 8dB to 24dB. So the margin of stability = 8dB,
and you just can't allow GNFB to ever be 24dB, even when the amp is unloaded. It means that you have to apply
the gain shelving networks just right because the margin of stability is exceeded first where there are peaks in
the sine wave response below 20Hz and above 20kHz. The best amps I built has 15dB GNFB which could be
increased to 35dB before oscillations could not be prevented by R&C networks for reductions of open loop
gain and phase shift below and above the audio band where the applied GNFB should effectively be reduced
because the open loop gain has been reduced. You do NOT want a high amount of GNFB applied at 10Hz
or 100kHz.

Some years ago I built a signal gene with switched sine wave F and switched square wave F.
Fig 1.
sheet-1-gene-sine-wave-wb-oscil-2Hz-200kHz-NE5534-13-2-2013.gif

Fig 2.
sheet-2-gene-square-wave-5-bjts-13-Feb-2013.GIF

Fig 3.
sheet-3-gene-sine-wave-wb-oscil-5-bjts-1Hz-1MHz-2-Feb-2013.GIF
Fig 3 above is another example of a wien bridge sine wave gene.

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