Oct 22, 2013

This article presents measurements and discussion of the push-pull power output stage for the vintage reissue Fender '65 Twin Reverb guitar amplifier model AB 763.

Items discussed include:

- a high-power dummy load for testing
- output tube bias conditions and achievable range
- using 2 power output tubes instead of the default 4
- plate dissipation limits and improper output loads
- measurement of output voltage, plate voltage/current and control-grid voltages
- load-line design and analysis for maximum power
- a push-pull calculator for power output and plate dissipation for any number of power tubes

This dummy load can also be used as a properly matched power shunt in combination with the standard 4 ohm speaker load. Since my TRR is quite clean (distortion-wise) even at higher powers with the stock Fender GT6L6B (Sovtek 5881) tubes, I typically use various distortion pedals to obtain my favorite overdrive sound. However the dummy load when used in a properly matched voltage divider network as shown below can be used in combination with the unmodified amplifier and speakers at high powers to achieve overdriven tube distortion but at much lower speaker volume levels.

The dummy load consists of eight 10 ohm power resistors rated at 25 W each in a switchable series/parallel combination as shown below. The SPST switch should be rated to at least 5A. This load produces an impedance of either 10 ohm (with switch as shown) using four resistors, or 5 ohm (with switch closed) using all eight resistors. For testing purposes these values are reasonable close to common nominal speaker loads of 8 or 4 ohms. [Additionally, two 50 ohm power resistors added in parallel on opposite sides of the switch would produce loads of 8.3 and 4.2 ohm] :

With this arrangement, a number of useful additional "taps" (not shown) become available for various interesting uses. Additional toggle switches or a rotary switch can easily be configured to facilitate load impedance selection over a broad range.

Ib(mA) Vg (volts) ------ ---------- 4 -61 (minimum "coldest" bias) 15 -53 (default shipping value) 33 -46 (nominal recommended value) 41 -43 (maximum "hottest" bias)For these tubes the "hottest" achievable bias current is 41mA which is well within the "safe" range of idle plate dissipation for this tube. Waveform tests below at a moderate power level only show cross-over distortion below 10 mA bias with no indication of any cross-over distortion at 15 mA, the default bias I measured for my new Twin. Several owners have reported that Fender ships tube amps with the bias set at a fairly low ("cold") level. The output waveform is slighly more rounded at 33 mA bias with no noticeable difference in shape (or preceived sound) between 33 mA and the maximum hottest bias of 41 mA. I perform the power tube bias test once a year. My '65 TRR was purchased new some 12 years ago. I have yet to replace any of the power tubes (but the 12AT7 driver tube became noisy after 1 year and needed replacement). The amp sounds comparable to when purchased. However I don't play frequently.

The setup used to test the amplifier with the dummy load using a USB function generator WGM-201 and dual channel oscilloscope DSO-101 from Syscomp Electronic Design is shown below. Suitable precautions were taken during all measurements to ensure the voltage input range of the DSO-101 was not exceeded. For these tests, the signal was applied to the reverb channel with bass, mid and treble settings at minimum and reverb/trem off. Driving a tube amplifier with a dummy load at very high levels can reveal audible mechanical vibrations at some frequencies (a buzzing sound). The twin speakers were disconnected as shown. Note that the "Int Speaker" jack MUST be used and NOT the Ext Speaker jack when a single speaker load connection is used. If no load is connected to the "Int Speaker" jack, the output transformer is shorted:

The scope trace below, with probes across the 5 ohm resistive dummy load with an 800mVpeak input signal at 250Hz corresponds to a fairly high output power of ~ 53 Wrms. There is negligible crossover distortion as expected for the bias point and the signal is fairly clean, as expected for the '65 TRR with not much evidence of tube saturation/distortion:

Randy Couch's excellent Designing Vacuum Tube Amplifiers and Related Topics discusses many interesting and useful aspects of tube amplifier design including non-idealities in the system. In the design, a power transform of sufficient size to handle the current levels at peak signal is selected with the turns-ratio chosen to provide the required Rpp value for the selected speaker load impedance Zl. For the '65 TRR amp, Np/Ns ~ 24 as measured directly by voltage ratio from plate-to-plate and transformer output.

Is it possible to lower the output power of the Twin Reverb amp and achieve greater tube distortion at the same drive levels by removing two power tubes?

If a pair of the power tubes (either the "inboard" set V8 and V9 or the "outboard" set V7 and V10) is removed this will produce an incorrectly "matched" driver output situation. Removing one tube on each side of the push-pull circuit requires the load impedance seen by the tube circuit to be twice as high to achieve a similar design point. If no other change is made except for removing a set of tubes, the remaining power tubes will be driving the SAME load impedance which is now too low by a factor of 2. The effective active load line for each tube is changed significantly and this will drive the plate dissipation beyond the safe limit for high signal levels (see detailed example below)! However the load impedance seen by the remaining two output tubes CAN be easily raised by a factor of 2 by

The measurements below using a 10X probe correspond to the maximum output swing levels (before clipping) for 3 cases. The upper case uses all 4 power tubes and a 5 ohm resistive load (close to the 4 ohm nominal speaker load) with output power (Vp)^2/(2*Zl) of 68 Wrms, somewhat lower than the specification of 85 Wrms for a 4 ohm load as expected.

Now consider the lower two measurements

where

Po(5ohm) = 36 Wrms and Po(10ohm) = 42 Wrms

For a given output load (5 or 10 ohms in this case), Rpp is given by the expression above using a turns ratio of 24 with:

Rpp(5ohm) = 2880 ohm and Rpp(10ohm) = 5760 ohm.

Imax can then be calculated and is found to be:

Imax(5ohm) = 316 mA and Imax(10ohm) = 242 mA.

The average power supplied to the push-pull circuit comprising both tubes for this maximum signal swing condition is:

This expression strictly applies to a half-wave rectified plate current as in class B operation but is reasonably accurate for class AB1 in which at maximum signal, each tube is cut-off for most of a 1/2 cycle as is the case for the TRR amplifier. At any rate it provides a good conservative margin for plate dissipation estimates.

With the measured plate supply voltage of Eo=455 VDC:

Psup(5ohm) = 91 Wrms and Psup(10ohm) = 70 Wrms.

The plate dissipation for maximum signal swing for EACH of the 2 tubes is then:

so Pdiss(5ohm) = 27.5 Wrms and Pdiss(10ohm) = 14 Wrms

per tube.

Note that although the power output Po to the load is somewhat LOWER for the 5 ohm load case compared to the 10 ohm load case, the actual total power supplied to the push-pull circuit Psup is considerably higher for the 5 ohm load case. Therefore there will be greater plate dissipation! The 14W rms plate dissipation for the 10 ohm load case for 2 tubes is well within the maximum plate dissipation range of 20-25W for the GT-6L6B (aka 5881). However with half that load of 5 ohm, the maximum signal swing plate dissipation of 27.5 Wrms is higher than the maximum allowable plate dissipation. This is directly a consequence of the modified load line due to a modified output load impedance.

To demonstrate typical signal shapes, a '65 TRR amp was used with 2 tubes and with a resistive load of 10 ohm (close to the 8 ohm optimum). The idle plate current was measured using a DVM and the GT bias tool to be 33 mA and the plate supply voltage at idle was 460 VDC as measured directly at pin 3 of an open socket. Although it is usually not necessary to measure and verify correct dynamic performance under signal, it is interesting to observe the signal shapes. This was accomplished by using 4 1Mohm 1/2 W resistors in series to realize a voltage divider as shown below which lowers the voltage measurement to about 1/4. For an overly conservative assumption of 200VDC maximum across each of the 1 Mohm resistors, each resistor would dissipate 40mW, well within the resistors power rating. This is used in combination with a 300VDC rated 10X scope probe and a USB dual channel scope.

The divider network and implementation is shown below. The tip of the divider was inserted into open tube socket pin 3 with the grounding clip attached. The combination of the voltage divider and a 10 Mohm scope probe has a conversion factor of 43:

The first plot below shows the simultaneous output voltage signals for a 250 Hz input sine signal across the 10 ohm load (blue) and the plate current (red) for one of the push-pull tubes as monitored using the GT bias tool which has a conversion factor of 1mA / 1mV. The tube is seen to conduct current for somewhat more than 1/2 of a complete cycle corresponding to Class AB1 operation. The peak current SWING above the quiescent plate bias current of 33 mA is about 160 mApeak. The power output to the 10 ohm load is about 15 Wrms, or about 1/3 the maximum power available with 2 tubes :

The traces below show the idle (zero input signal) voltages:

Finally the traces below show the plate voltage

Although the tube conducts substantially for only half a cycle, notice that the plate voltage continues to rise above the nominal plate voltage value of 460 VDC (the green T line in the picture) to a peak value of 645 VDC during the tube's cutoff region. The reason for this is found in the operation of the center-tap transformer: For the tube shown, during its "cutoff" section where little plate current flows, the OTHER tube is driving the OTHER side of the transformer primary (which is half the primary turns). This generates output current in the load connected to the secondary of the transformer. This signal generated by the other active tube will of course transform back to the FIRST tube circuit (call it a "back emf") since the transformer secondary turns overlap both halves of the primary turns. This will therefore increase the plate voltage of the "cut-off" tube (think of it as a temporarily open circuit) with a voltage profile that looks very similar to that seen on the conducting active tube. The part of the tube's plate voltage swing which actively creates the output signal is the decreasing part (roughly below 460 VDC) during which that tube is conducting. From the diagram, this peak voltage swing (below 460 VDC) is seen to be 5*43 = 215 Vpeak (where 43 is the conversion factor for the voltage divider and 10X scope probe). The other tube has a similar swing also below 460 VDC but drives the other half of the transformer with current in the opposite direction in the winding thus creating an inverted output signal and creating a full sine output signal. Each plate during its conducting half-cycle drives half the primary coil. Therefore for this example, the primary 215 V peak swing transforms to the secondary as 215/12 = 18 Vpeak in agreement with the peak output voltage measured above.

The blue traces below show the control-grid signals for the 2 power output tubes under near-maximum output power as monitored with a 10X probe at open socket pin 5. The voltage divider used above for Vp measurements was not required due to the smaller grid voltage levels. Input signal level to the amplifier (red) was ~ 800 mVpeak and the amp controls were adjusted to achieve maximum output level to the resistive load. The idle (no signal) control-grid voltage was -46 VDC (for quiescent tube bias Iq = 33 mA). The control grid voltage swings to 0V at the peak of the tubes conducting phase to ~ -85 VDC at maximum cutoff. The control-grid signals are inverted in phase as shown:

The sketch below shows qualitatively the various voltages, currents and Q point as measured for an audio cycle under typical bias conditions for the '65 TRR amplifier and with a maximum input voltage swing. It pictorially shows how each power tube, during its strong conducting half-cycle, contributes piece-wise to the transformer output waveform:

The load-line is drawn through the point Vp = Vb = 455VDC and through the knee of the plate characteristic for Vg2 ~ 450VDC for maximum the grid voltage Vg1 = 0. The slope of this curve 455V/0.415A = 1096 ohm is the load line resistance RL for each tube driving half the primary winding. This resistance is 1/4 of the plate-to-plate resistance so Rpp ~ 4.4 kohm. With the output transformer of the TRR amp having a turns ratio of 24, the required output load, through reflection is therefore 7.6 ohm which is close to the 8 ohm load as discussed earlier for two tubes. The maximum RMS power output

where Vmin = 60 V, Vmax = Vb = 455 V and Imax = 370 mA as shown in the graph. Therefore, for 2 tubes and the ideal 7.6 ohm output load (4.4 kohm Rpp load), the maximum power output expected into the transformer primary is ~ 73 W. I tested my TRR amplifier under a resistive load of 8.3 ohm (which changes the calculated maximum power output to ~ 70W). Under maximum output signal level, the voltage swing was measured to be (Vb - Vmin) ~ 353 V and the maximum plate current was directly measured to be 370 mA which leads to a measured primary power output of ~ 65 W which considering the model is quite close to the predicted 70 W value. This is the power delivered to the transformer primary. The actual output power to the resistive load on the transformer secondary will of course be less due to transformer losses. The measured maximum output signal at the 8.3 ohm load was V= 28 Vpeak which corresponds to an RMS output power of 47 W.

The plate dissipation of each tube can be predicted for any location on the load-line curve (not just the maximum power case) or determined using the measured plate current and voltage values at the transformer primary. It is simply 1/2(total input power - power delivered to the primary load):

The expression for Pin is strictly speaking for class B half-wave plate current shape but it provides a worst-case conservative estimate of supplied power and plate dissipation.

[Note: It is important to recall that the power dissipation per tube may NOT necessarily be at its greatest value for the maximum power output point on the load line. In fact, the plate voltage swing which leads to the greatest plate dissipation is (Vb - Vmin) = 2/πVb = 0.64Vb (or equivalently Vmin=0.36Vb). Therefore if Vmin at the intersection point with the plate characteristic is lower than 0.36Vb, the calculated Pdiss using this Vmin value will underestimate the actual maximum plate dissipation which will occur for voltage swings less than the maximum possible value. However for simplicity in the calculations below, Pdiss will be computed for the maximum power output intersection point shown above. See the section below for more detail and the correction factor.]

For the design example above, the total power input is 107 W and the maximum power output into the transformer primary load is 73 W so the power dissipation of each tube at maximum output power is 17 W which is within the maximum plate dissipation spec for this tube (~ 25 - 30 W). [The actual maximum dissipation 0.36Vb point on the load line is 164V for which the plate dissipation is slightly higher at 19.5 W but still within the dissipation specification.]

The above load line analysis has been done for a push-pull output with two tubes, one on each side of the push-pull circuit. If each tube is doubled in parallel (as in the '65 TRR amp with all 4 power tubes), the maximum power analysis doesn't need to be repeated as it is identical to that above

As a useful perspective, the chart below shows predicted power results for the '65 TRR amp, using the 6L6GC plate characteristics above, for exact 4 and 8 ohm output resistive loads and an ideal output transformer. The numbers only include plate and load power dissipations and are for the maximum signal swing (to Vg1=0 for class AB1 operation). The final column shows the output load power assuming a reasonable 70% power transmission through the output transformer:

Pin(total) Pout(tot) Pdiss(per tube) Pout(70%) ---------- ---------- --------------- --------- 2 Tubes 4 ohm 120 W 46 W 37 W 32 W 8 ohm 101 W 71 W 15 W 50 W 4 Tubes 4 ohm 202 W 142 W 15 W 99 W 8 ohm 104 W 75 W 7 W 53 WNote the excessive power dissipation

The charts below show a typical load line with the quantities defined (as above), and the plate dissipation (relative to the maximum possible value) for any voltage limit on the load line Vmin/Vb. As mentioned, for Vmin values greater than 0.36Vb, as will be the case for triodes with typical load lines, no correction is needed. For Vmin values lower than 0.36Vb, which is frequently the case for pentode characteristics designed properly for maximum power, the curve can be used to determine the correction factor. This is applied to dissipation calculated based on the maximum power output to obtain the true maximum plate dissipation (or the exact expression above can be used).

- In all cases, enter Tubes, Vb, Vmin and ZL
- Enter Imax and click
**Use Imax**. RL and Np/Ns will be calculated/updated and the power fields updated - Enter RL and click
**Use RL**. Imax and Np/Ns will be calculated/updated and the power fields updated. - Enter Np/Ns and click
**Use Np/Ns & ZL**. RL and Imax will be calculated/updated and the power fields updated.

Parameters:

**Tubes**total number of tubes in push-pull circuit

**Vb**plate supply soltage

**Vmin**minimum voltage (maximum swing) along load line

**Imax**maximum current per tube along load line corresponding to Vmin

**RL**primary load resistance for half push-pull circuit = 1/4(Np/Ns)^2ZL

**Np/Ns**primary to secondary turns ratio for output transformer

**ZL**output load impedance

**Psupply**total power supplied to entire push-pull circuit

**Pout**total output power into transformer primary

**Pdiss**=(Psupply - Pout)/Tubes power dissipation per tube for signal swing to Vmin, Imax.

**Vmin (lower)**minimum voltage along load line for maximum plate dissipation

**Pdiss_max**maximum possible plate dissipation per tube

To determine the load line slope which provides the maximum achievable Po value, we assume the Vg1=0 plate characteristic follows a 3/2 power Child's law shape for thermionic emission from a cathode. Then using some basic calculus, it is easy to find the intersection point corresponding to maximum output power and to prove that it really is a maximum power point:

where A is some constant which depends on the tube details.

The power ouput Po corresponding to any intersection point (any load resistance and Vb value) is:

The rate of change of Po is zero at the maximum Po value. Differentiating with respect to the intersection point Vmin and setting the result to zero:

Solving for the value of Vmin which provides maximun Po:

To verify that this is a maximum (and not minimum or saddle point) we examine the sign of the second derivative at the critical value above:

and since this is always a negative value, we indeed have found a MAXIMUM Po value.

The slope of the load line at this maximum power point Vmin=0.6Vb is obviously -Imax/0.4Vb and it is easy to show that the slope of the plate characteristic curve at the maximim power intersection point (dashed green line) is just the negative of this Imax/0.4Vb = 1/RL where RL=1/4Rpp is the load resistance corresponding to this load line. For 2 triodes and a load line chosen for this maximum output power intersection at 0.60Vb, the maximum power output (both tubes) is:

and the corresponding power dissipation per tube for the intersection point is:

Thus at this maximum power point, the power output for both tubes and power dissipation per tube are nearly identical.

A more accurate analysis (see Radio Designer's Handbook) of triodes in push-pull uses the actual "composite characteristic" of both tubes (difference current of both tubes). The composite characteristic has a nearly linear slope (compared to the single triode 3/2 power law shape) with a slope value which will be very nearly the same as the local slope (dashed green line) shown above for maximum power output using a single triode characteristic. This is true because at the maximum power output point, one of the tubes will be at cutoff so the slope will be that of a single conducting tube. It is easy to show, using an analysis identical to that above, that for such a perfectly linear "composite characteristic", the maximum power intersection point corresponds to equal slopes for the composite characteristic and load line. It is therefore intuitively obvious that for a pentode under typical design conditions, the maximum power will again be given by the point of equal slope intersection. In this case however, since the pentode characteristic has a sharp knee at low voltage, the slope of the Vg1=0 plate characteristic curve corresponding to maximum power in AB1 service will change very rapidly at the knee. Thus the equal slope location (at Vmin and Imax) will occur approximately at the knee position.

- RCA Receiving Tube Manual, Technical Series RC-21, 1961, p.23
- Radio Designer's Handbook, Ed. F. Langford-Smith, 4th Corrected Edn. 1957, Ch 13.6
**Push-pull pentodes and beam power amplifiers**, Class A, AB1", p. 583. - Designing Vacuum Tube Amplifiers and Related Topics, 2nd Edn, Randy Couch, 2013
- The Tube Amp Book, Aspen Pittman, 4.1th Edn., 1995
- Bias Kit Manual, Groove Tubes LLC, 1999
- Inside The Fender '65 Twin Reverb Reissue Amp