Empirical implementation of global negative feedback.

by

Tim E. Smith.

Typically, to successfully implement or derive a global negative feedback loop for a tube amplifier you need a signal generator which can provide sine and square waves, a dual channel or dual trace oscilloscope, an good DMM, and a capacitance meter that can measure small capacitance down to 10 pf or so. It is also a very good idea to have a 5 or 10 amp variable AC transformer ("variac") to slowly bring the amplifier up to normal input voltage (120 volts). Additionally, the amplifier under test should be stable in open-loop configuration and have its output tubes set at the desired idle current. All of these are not overly expensive and should be part of a designer's test set. If a scope isn't available, a good quality DMM that can accurately read AC voltage may suffice.

It is strongly suggested that you build a small feedback implementation device consisting of a 50k linear pot paralleled with an adjustable capacitor with range of 0 - 500 pf, either a trimmer cap or a variable capacitor from an old tube radio will suffice. (The purpose of the capacitor is to reduce closed loop gain to less than one at a frequency below which the amp output is 180 or more degrees out of phase with the input. This prevents oscillation.) This circuit should have two wires coming out of it for connection to the amplifier, and should be switchable so it can be turned on or off.

Figure 1. Feedback (yellow wires) and snubber (red wires) test set. This consists of a 50 k pot and 500 pf trimmer which here has a 470 pf cap wired in parallel with it with a DPDT switch that simultaneously closes the feedback loop and engages the capacitor. When it is opened the loop is opened and both the resistance of the pot and capacitance can be measured. The yellow wires leading away to the left will be connected to the amplifier. The red wires are associated with the input tube snubber mentioned later.

The feedback will be derived from the output tap of the amplifier while the cathode circuit of the amplifier's input stage will be the injection point for the feedback loop. For the feedback method described here, the cathode circuit should consist of three elements, a resistor bypassed by a capacitor, connected to a smaller value resistor (perhaps 1/4 to 1/10 the value of the bypassed resistor) which in turn is connected to ground. The feedback signal will be fed injected at the junction of the two resistors (Figure 2).

The input tube should have its plate and total cathode resistors set so that cathode voltage is around 1.5 volts (or more); this prevents small amounts of grid current that tend to appear from grid to cathode at voltages of about 1 volt or less. For one triode of a 12AX7 and small pentodes like 6AU6 and EF86, the total cathode resistance will likely be in the vicinity of 1 k ohm, accordingly, a suitable arrangement for the cathode resistance maybe something like 910 ohms bypassed by 75-200 uf, connected to an unbypassed 100 ohm resistor to ground. The ratio of bypassed to unbypassed resistance will determine the gain of the input stage. I like ratios of about 4 to 10 to 1 to preserve most of the gain of the input stage while providing a feedback injection point. Note that the feedback resistor will be in parallel with the lower cathode resistor and reduce its effective value, however, the feedback resistor will typically be 20 to 30 times greater than the unbypassed cathode resistor. In the case provided by Figure 2, the actual unbypassed cathode resistance will be about 230 ohms, a negligible difference from the 240 ohms placed in the cathode circuit.

Figure 2. Amplifier circuit showing feedback, snubbers, and local feedback resistors. The output transformer snubber is "hard wired", while the input tube snubber and feedback are adjusted on test with the test set shown in Figure 1. This amplifier uses switchable feedback for use with the 4 or 8 ohm output.

It's important to note Max's golden rule of negative feedback: Build the best amplifier you can and then linearize/stabilize it with an appropriate amount of global (and maybe local) feedback. To this end, it's important to optimize the operating points of all tubes in the circuit, and use a quality output transformer that will allow useful amount of feedback around it.

The actual setting of the feedback will require that the amp is operational which carries with it the hazards of accidental exposure to high voltage. Always be careful! When working near an energized amplifier, only use one hand, wear rubber shoes, and stand on plywood or a rubber mat! To use the circuit shown in Figure 1, make sure that the amp is off and unplugged, solder one wire to the appropriate output (perhaps the 8 ohm setting) and the other wire to the feedback injection point in the cathode circuit of the input tube (note that you will be setting the feedback for one channel only, hopefully the other channel will respond to the feedback that is calculated for this channel). Turn the feedback switch on the circuit off and set the pot at full resistance (50k), and set the bypass cap on it to around 500 pf. Once this is done, connect 10 to 20 watt 8 (or 7.5 to 8.2) ohm power resistors to both 8 ohm outputs (stereo amp, both channels will be on). Then connect one scope probe to the hot side of the 8 ohm resistor and the other to the grid of the input tube. Next, connect the signal generator to the amp's input (the channel that is going to be used to set the feedback). Check and re-check all connections. These steps are listed below:

Once all of this is done, bring the amplifier up to full AC input (120 volts). Set the signal generator to about 2 kHz, sine wave. Advance the generator output and/or amplifier volume to produce an 8 volt peak-peak display on the scope from the probe attached to the 8 ohm power resistor (8 volts peak-peak into 8 ohms equals 1 watt). Now check the amplitude of the input signal (probe at the input tube grid). The ratio of these two voltages will be the open loop gain of the amplifier, and help determine how much feedback is desired or can be applied. Typically it is hard to enclose a tube amplifier with much more than 20 db of negative feedback (10 fold reduction in output after the loop is closed) and maintain stability. That sets an upper limit to the amount that can be applied.

Let the amplifier warm up for a few minutes. Now for the moment of truth. Flip the switch on the feedback circuit so it is on, and check the output on the scope display. It should either go down some, maybe by 25 to 50%, or increase, or go into oscillation (the scope screen goes blurry). Either of the last two are bad. Turn the amp off. Increase in output or oscillation indicate that the output transformer primary leads must be switched from tube to tube in a push-pull amp. In a single-ended amplifier either the primary or secondary must be reversed but not both. Once the feedback has been established with the pot at 50k, slowly rotate the pot to get about a five-fold reduction (about 14 db); hopefully the amp will remain stable. Now switch the generator to square wave output and check the leading edge of the square wave response. It may be slightly ringy or pretty good. Increase the generator frequency to about 10 kHz. You'll likely find that the bypass cap on the 50k pot needs to be adjusted some to minimize ringing, or lessen the slope of the leading edge. Now go back to 2kHz and re-set to sine wave output. Slowly rotate the 50k pot to get an 8-fold reduction (1 v P-P on the scope), corresponding to 18 db of negative feedback. Now switch to square wave and sweep through 2 to about 10 kHz. You'll probably find that the square wave has become more ringy or ragged, and can't be fully compensated by adjusting the 50k pot's bypass capacitor (as a rule of thumb, around 680 pf will come pretty close).

Now comes the time to think about some HF compensation to help stabilize the amplifier and allow up to 20 db of negative feedback. It's pretty easy to provide some HF compensation in the amplifier (within the negative feedback loop) by applying two small snubber circuits. Snubbers are simple high cut circuits that employ a resistor and small capacitor in series. The first application is a snubber across each half of the output transformer primary. It turns out (from the Radiotron Designer's Handbook, 4th edition and David Wolze, Glass Audio, 3, 1995, p 18-19) that appropriate values for each half are a resistor equal to the primary impedance and a capacitor equal (or close) to the reciprocal of that impedance divided by 100,000.

R = plate to plate impedance.

C = 1 / (100,000 x plate to plate impedance).

For a 5000 ohm output push-pull transformer, the values for each half would be a 5.1k 5 watt resistor in series with a 2 nf capacitor; for a 7600 ohm transformer, the values would be a 7.5k 5 watt resistor and a 1.5 nf capacitor. For a single end transformer, the resistor value is equal to the transformer's primary and the capacitor value equals the reciprocal of the impedance divided by 100,000 (from experience). For a 5 k single ended transformer the values would be the same as calculate above for the push pull but there would be only one network across the primary.

Editor's note: There is an inconsistency here. Due to the fact that the impedance of a transformer changes as the square of the turns ratio, the impedance of half of the primary is ¼ the total impedance. Applying this to the two snubbers the resistor should be 1250 ohms and the capacitor should be 8 nf. Tim has checked his sources and he has confirmed that he is quoting them correctly. If you wish to pursue this issue, take it up with the sources not with Tim.

Obviously connect these while the amplifier is powered off! The other snubber is a small circuit that can be used to bypass the input tube's plate resistor (to decrease gain at high frequencies), or provide an HF short from the input tube's plate to ground. I built an adjustable snubber circuit on the same board as the feedback circuit mentioned earlier (Figure 1), but this has to be used with care! Unlike the feedback circuit which does not carry dangerous voltages, this one does! - either the plate voltage of the input tube, its B+ supply (much more dangerous!), or the grid of the splitter (Figure 2). For safety's sake, I much prefer the connection from the input tube's plate or splitter input to ground, but you may need to try all three configurations to see which works best. This circuit, like the feedback circuit, uses a 50k linear pot and 0-500 pf adjustable capacitor, but connected in series, not parallel. Additionally, I apply a small amount of local feedback from output tube plates to splitter plates via 3 watt resistors rated at about 12-15 times the resistance of the splitter plate resistors (Figure 2). This technique only works with inverter circuits in which the signals are taken off of the plates of two identical triodes such as the long tail pair.

With amplifier powered up, and using very considerable caution (remember that the input tube snubber carries high voltage), adjust the feedback pot to get 10-fold reduction (20 db) - if you want that much. Then set the generator to square wave, and optimize the result by adjusting the snubber pot and capacitor, along with the feedback capacitor. The feedback pot will not be changed. Once you are satisfied with the result, power the amplifier down, wait about 10 minutes for the power supply capacitors to discharge, and then measure all of the adjusting components: feedback resistance, feedback capacitor, snubber resistance, and snubber capacitance, and then solder their equivalents into the circuit. It is usually possible to get close enough with 5% components, but if desired, 1% resistors are easily available from Mouser or Digi-Key. Note - if you are rightfully concerned about the high voltages associated with the snubber, it's been my experience that 10 to 15k and 150 to 200 pf work well. Using the techniques mentioned above, I have been able to get quite good square wave response at 1,3, and 10 kHz with 20 db of global feedback, shown in Figure 3, taken from a 25 watt/channel EL84 amplifier. Some may say that this amplifier has too much roll off at high frequencies (about 1.5 db at 20 kHz), but the amplifier is very stable and has an alluring sound (so my friends say).

Only a tiny minority of adults can hear 20 kHz. Even for those who can, 1.5 dB is hardly noticeable. Systems that are flat out to 20 kHz are of interest only to babies and dogs.

Obviously, this is not the right answer, it's just an answer that suits the desires of the designer. Someone else may want more HF extension, but this will usually come with some ringing or raggedness evident in the 10 kHz square wave's leading edge. Many of the tube amplifiers reviewed in Stereophile have fairly ragged or ringy 10kHz square wave responses. Personally I like the very gently rolled-off high frequencies and think that this may lead to reduced listener fatigue. This does imply that the amplifier becomes something of an involuntary tone control, but such a characteristic is inherent in any amplifier that has high output impedance (>1 ohm at the 8 ohm tap), typical of many or most tube amplifiers.

Figure 3. Square wave responses: left - 1 kHz, center - 3 kHz, right - 10 kHz. There is no ringing, indicative of potential HF instability.

Essentially all of this work has been focused on providing three separate HF roll offs to accommodate high frequency characteristics of the output transformer (Max could provide appropriate mathematical rigor as he has in his website, the results described here are all empirically derived). Morgan Jones would call the techniques mentioned here "slugging the dominant pole", basically hammering the HF instability of the output transformer with a cascade of HF roll offs. Most good output transformers will work well, I've had very good results with off-the-shelf Hammond units and the custom ones I have wound by Heyboer. I've had considerable difficulty with many Edcors and never really been satisfied with the results, although the smaller ones seem to work better.

Tim Smith

This page last updated July 24, 2014.

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