Idle Current Biasing - Why 70 percent?

General

When biasing using the idle current method, most people recommend using 70% of the maximum plate dissipation for the tube in question as the upper limit.  Why 70%, and not 50% as some others recommend?  Is there any science behind this, or is this just a number "pulled out of the air" as some have suggested?   Is this indeed a "safe" method of biasing?
How is plate dissipation determined?
Plate dissipation in a tube is a function of the voltage drop across the plate-to-cathode elements of the tube and the current through the tube.   Plate dissipation follows Ohm's law, in that the power is equal to the voltage multiplied by the current.

There are three different dissipation types to consider - idle dissipation, instantaneous dissipation with signal applied, and average dissipation with signal applied.  Idle dissipation is simply the product of the plate voltage and plate current at idle, i.e., when no signal is applied.   This is easily measured and calculated.  Instantaneous plate dissipation is a bit trickier, because it changes throughout the cycle of the input waveform.  It is again the product of the plate voltage and plate current at any given point in time, hence the name "instantaneous" plate dissipation.  Average dissipation is what really counts in most tube amp designs.  It is the time-average of the instantaneous dissipations over the input cycle.   Since the plate element has a certain amount of thermal mass, average dissipation is what counts.  A tube's maximum plate dissipation can be exceeded at some point during the cycle, provided that it is far enough below the maximum dissipation during other parts of the cycle for the average dissipation to not exceed the tube's max plate dissipation rating.

It is a common misconception that maximum plate dissipation occurs at maximum power.  Another common misconception is that the worst-case dissipation occurs at a full-power square wave. This is usually the source of the 50% max dissipation limit put forth by those who don't really understand what is going on.   Actually, a full-power square wave results in the least plate dissipation.  This is because the plate voltage and plate current are out of phase, i.e., when the plate voltage is at a maximum, the plate current is at a minimum.  Taken to the extreme, at full power square wave output, the plate voltage will swing from a minimum of zero to a maximum of twice the idle plate voltage, and the plate current will swing from a minimum of zero to a maximum value of the plate voltage divided by the plate load resistance (all voltage/current swings must follow the load line set by the output transformer's reflected impedance). Since the product of the plate voltage multiplied by the plate current is zero for all parts of the square wave cycle, the average plate dissipation is zero, certainly not 50%!    There is a class of amplifiers designed to take advantage of this low dissipation and ultra-high efficiency, known as "class D" amplifiers.  Since the output devices are always either full on or full off, the only time the output devices are dissipating any appreciable power is during the switching time.

There are three factors to take into account in determining a maximum "safe" operating area for a tube:  plate voltage, idle current, and the load impedance the tube is working into.  The first two determine the static, or idle dissipation, and all three determine the average active dissipation under signal.  As long as the maximum plate dissipation for a tube is not exceeded at idle or under all signal levels from zero signal to maximum clip, it is operating in the "safe operating area" for that tube.
Okay, so how do we determine the safe operating area?

As mentioned previously, it is a simple matter to determine if the idle dissipation is exceeding the maximum plate dissipation specs.  Why can't we just set the idle dissipation at max and be done with it?  In some cases, you can.  In a true class A amplifier, you can bias at maximum plate dissipation because idle is the point of maximum active dissipation - the dissipation in the tube actually decreases throughout the entire range of operation, so you are in no danger of exceeding the tube specifications if you bias for maximum dissipation at idle.  However, in a class B or class AB amplifier, the dissipation increases with applied signal up to a maximum at some point in the operating range (not necessarily full power).  If you know the plate voltage and the load impedance the tube is working into, you can determine a maximum idle current that will insure the tube dissipation ratings are not exceeded at any point in the operation.   The idle current sets the point at which the plate current cuts off on the negative-going swing of the cycle.  In a class B amplifier, the idle current is zero, so the plate current only flows during half the cycle.  If you raise the idle current (to decrease crossover distortion and/or change the tone and distortion characteristics of the amp), the plate current will flow for a longer period of time during the cycle.  The plate load impedance is extremely important, as it sets the maximum average plate dissipation under signal conditions, and thus, the maximum idle current that can be used.

Following are some examples of average plate dissipations for different plate voltages, plate load impedances, and idle currents.  The graphs show the average plate dissipation in two hundred steps of peak plate voltage swing, ranging from zero (idle plate voltage) up to Vpp (resulting in a maximum peak-to-peak voltage swing of twice the idle plate voltage, from zero to 2*Vpp, corresponding to max and min currents on the load line).  These graphs show the variations in plate dissipation for various signal swings.   The graph idle currents and load impedances were chosen to match a 25W max plate dissipation, such as for a typical EL34 output tube.   The curves were generated with a custom program developed specifically to determine safe operating area of a tube based on given circuit data.1

This first image shows the average sine wave dissipation of a tube running at 450V plate voltage and 39mA idle current (chosen by the "70%" rule assuming a maximum desired plate dissipation of 25W) into a 1.25K load (an effective 5K plate-to-plate push-pull load in class AB1).  As can be seen from the image, the maximum dissipation does not occur at full output power, rather somewhere just above a midscale voltage swing at the plate.  The maximum average sinewave dissipation occurs near midscale, at around 22.5W, well within the safe operating area of the tube.  It decreases to around 14W at full output power.

The second image shows the average square wave dissipation of a tube running at the same conditions as above.  As can be seen from the image, the maximum dissipation again does not occur at full output power, rather somewhere just above a midscale voltage swing at the plate.  The maximum average squarewave dissipation is around 24.8W, again within the safe operating area of the tube, and decreases to zero at full power squarewave output.

This next image shows the average sine wave dissipation of a tube running in class A at 250V plate voltage and 100mA idle current (chosen by the "100%" rule for class A, assuming a maximum desired plate dissipation of 25W) into a 2.5K load.  As can be seen from the image, the maximum dissipation does not occur at full output power, rather at idle.  The maximum average dissipation is 25W at idle and drops to around 12.5W at full power.

This next image shows the average square wave dissipation of at tube running in the same class A conditions as shown above.  As can be seen from the image, the maximum dissipation again does not occur at full output power, rather at idle.  The maximum average dissipation is 25W at idle and drops to zero at full power.

This next image shows the average sine wave dissipation of a tube running in class AB1 at 380V plate voltage and 46mA idle current (chosen by the "70%" rule for class AB, assuming a maximum desired plate dissipation of 25W) into a 1K load (4k p-p).  As can be seen from the image, the maximum dissipation again does not occur at full output power, but somewhere just above midscale.  The maximum average dissipation is 17.5W at idle and increases to 20.7W at midscale, and drops back down to around 13W at full power.

This next image shows the average square wave dissipation of a tube running at the same conditions as above.  As can be seen from the image, the maximum dissipation again does not occur at full output power, but somewhere just below midscale.  The maximum average dissipation is 17.5W at idle and increases to 22.7W at midscale, and drops back down to zero at full power.

This next two images show the results of designing an amplifier with too low a plate load impedance for the plate voltage.   If the plate voltage is very high, the plate load impedance must be increased to avoid exceeding the maximum average tube dissipation.  If these tubes were biased using the 70% method, they would exceed the dissipation throughout much of their range.  In fact, even when biased at class B, or zero idle current, these tubes will exceed their dissipation by almost 8W at some points in their operation.  It is sometimes possible to safely run an amplifier that has it's high point excursion above the average dissipation for the tubes, because, on average, the amplifier is not running in the max dissipation range continuously.  Possible, but not a good idea for tube longevity.

This next image shows the same plate voltage, same idle current as the two images above, but with a more reasonable 1.9K plate load (7.6K p-p in push-pull).  Now, the 70% biasing method will work, as the dissipation never exceeds 25W for either sine or square wave signals.

Conclusions:
As can be seen from the graphs, the maximum allowable idle current varies with plate voltage and plate load impedance (and by virtue of these two parameters, class of operation).  If the plate load impedance and plate voltage are known, a maximum idle current can be determined to insure the average dissipation never exceeds the maximum specification of the tube over all output voltage swings.  A good tube amp designer will determine the safe operating area of the output tubes and publish a recommended maximum idle current to keep the amplifier in the safe area.   If the plate load impedance is not known, setting the bias to 70% of the maximum allowable dissipation is usually a safe spot for a class AB amplifier, as shown by the graphs.   This "rule-of-thumb" will work in most cases for commercial guitar amplifiers.  The only place it will fail is for amps that have very low plate load impedances or extremely high plate voltages without correspondingly high plate impedances, but in these cases, other biasing methods will likely fail as well.  Setting the bias to 50% of the maximum plate dissipation will usually result in too conservative a setting.

It is important that the tube amp designers take it upon themselves to provide biasing and safe operating area information in the tech manual for the amplifier and insure that the design doesn't greatly exceed tube operating parameters if they want to insure a decent tube lifespan.

Appendix A:  The program used to develop the graphs shown in this paper

1Following is a screenshot of the C++ program used to develop the graphs shown in this paper.  It is a work-in-progress at the moment.  The tube parameters are input on the left-hand pane and the output parameters are calculated and displayed in the right-hand pane.  In addition to displaying the max data, a number of data points are written out to a text file to allow charting of data trends.  The graphs shown in this paper were made by importing this data into a Microsoft Excel spreadsheet and charting the results.  Max average dissipation points were verified in PSpice simulations using EL34 tube models.

Copyright ©  2003  Randall Aiken.  May not be reproduced in any form without written approval from Aiken Amplification.

Revised 02/11/03