2A3: plate res = 800 ohms, load = 2500 ohms
45 @250V: plate = 1610, load = 3000
6L6 (triode connected, fixed bias): plate = 1700, load = 5000
Theoretically, the maximum power transfer to the speaker occurs when the plate resistance and load resistance are equal. In practice, however, there are other factors that change the equation - but I can't recall the explanation. Something to do with frequency response, perhaps?
I've emailed you Chapter 7 from THEORY AND APPLICATIONS of ELECTRON TUBES by Heebert J Reich, Ph.D. This chapter provides some good theroy on Class A and Class AB1 power amplifiers, there is a good discussion on plate resistance / load.
Gary
:The recommended load resistance for an audio power triode is often 2 or 3 times the plate resistance. For example, here is data from an old (c. 1942) tube manual for single-ended power amps:
:
:2A3: plate res = 800 ohms, load = 2500 ohms
:
:45 @250V: plate = 1610, load = 3000
:
:6L6 (triode connected, fixed bias): plate = 1700, load = 5000
:
:Theoretically, the maximum power transfer to the speaker occurs when the plate resistance and load resistance are equal. In practice, however, there are other factors that change the equation - but I can't recall the explanation. Something to do with frequency response, perhaps?
:
:
After I clicked on the "Submit Follow Up" I noticed several errors in my message and just had to send a corrected version.
I've emailed you Chapter 7 from THEORY AND APPLICATIONS of ELECTRON TUBES by Herbert J Reich, Ph.D. This chapter provides some good theory on Class A and Class AB1 power amplifiers. There is a good discussion on plate resistance / load.
Gary
:The recommended load resistance for an audio power triode is often 2 or 3 times the plate resistance. For example, here is data from an old (c. 1942) tube manual for single-ended power amps:
:
:2A3: plate res = 800 ohms, load = 2500 ohms
:
:45 @250V: plate = 1610, load = 3000
:
:6L6 (triode connected, fixed bias): plate = 1700, load = 5000
:
:Theoretically, the maximum power transfer to the speaker occurs when the plate resistance and load resistance are equal. In practice, however, there are other factors that change the equation - but I can't recall the explanation. Something to do with frequency response, perhaps?
:
:
It's well known that if there is a voltage source (like, for example, a battery) that has in internal resistance, the maximum power to a load will occur when the load resistance is equal to the internal source resistance. This might lead you to think that for a triode power tube, the load resistance should be equal to the plate resistance for max power to the speakers.
The thing that needs to be considered is that unlike a battery, a tube's output isn't limited by a fixed voltage source - rather, it's limited by the maximum allowable plate dissipation (plate current). So, if the load resistance is increased above the plate resistance, the plate current will drop, right? Well, then you can re-jigger the grid bias and grid-voltage swing to restore the plate current to the maximum. Etc., etc.
The result is that the load resistance can be jacked up to 2x of the plate resistance, at which point the power transfer to the load is maximized.
In the case of a battery, the limitation is a fixed ideal voltage source. But if the battery's output were limited, instead, by the allowable dissipation in its internal resistance, and the voltage source were variable, then the optimum load resistance would be higher, 2x in fact. As you raise the load resistance, you would be able to jack up the voltage source to maintain max current.
If you want to see the math, ask Gary for the reprint.
The idea of setting the load resistance equal to twice the plate resistance is somewhat of an approximation, depending upon the linearity of the plate characterisic curves. And, for pentodes, things become quite a bit different, unless they are triode connected (screen connected to plate).
Now that I sort of understand this, I can now move on to some of the multitude of other things that puzzle me!
Doug
:
:Hi Doug,
:
:I've emailed you Chapter 7 from THEORY AND APPLICATIONS of ELECTRON TUBES by Herbert J Reich, Ph.D. This chapter provides some good theory on Class A and Class AB1 power amplifiers. There is a good discussion on plate resistance / load.
:
:Gary
:
:
:
::The recommended load resistance for an audio power triode is often 2 or 3 times the plate resistance. For example, here is data from an old (c. 1942) tube manual for single-ended power amps:
::
::2A3: plate res = 800 ohms, load = 2500 ohms
::
::45 @250V: plate = 1610, load = 3000
::
::6L6 (triode connected, fixed bias): plate = 1700, load = 5000
::
::Theoretically, the maximum power transfer to the speaker occurs when the plate resistance and load resistance are equal. In practice, however, there are other factors that change the equation - but I can't recall the explanation. Something to do with frequency response, perhaps?
::
::
You got me thinking, what techniques are used to "re-jigger" the grid voltage?
I believe Inverse Feedback is used, where a portion of the audio output is fed back to the grid to lower the source impedance of the circuit, reducing distortion. This is especially true when the load is a loudspeaker, where the load impedance varies with frequency.
Gary
:I reviewed the reprint from Gary - some calculus and general hand-waving. But, I now think I understand the answer to my question.
:
:It's well known that if there is a voltage source (like, for example, a battery) that has in internal resistance, the maximum power to a load will occur when the load resistance is equal to the internal source resistance. This might lead you to think that for a triode power tube, the load resistance should be equal to the plate resistance for max power to the speakers.
:
:The thing that needs to be considered is that unlike a battery, a tube's output isn't limited by a fixed voltage source - rather, it's limited by the maximum allowable plate dissipation (plate current). So, if the load resistance is increased above the plate resistance, the plate current will drop, right? Well, then you can re-jigger the grid bias and grid-voltage swing to restore the plate current to the maximum. Etc., etc.
:
:The result is that the load resistance can be jacked up to 2x of the plate resistance, at which point the power transfer to the load is maximized.
:
:In the case of a battery, the limitation is a fixed ideal voltage source. But if the battery's output were limited, instead, by the allowable dissipation in its internal resistance, and the voltage source were variable, then the optimum load resistance would be higher, 2x in fact. As you raise the load resistance, you would be able to jack up the voltage source to maintain max current.
:
:If you want to see the math, ask Gary for the reprint.
:
:The idea of setting the load resistance equal to twice the plate resistance is somewhat of an approximation, depending upon the linearity of the plate characterisic curves. And, for pentodes, things become quite a bit different, unless they are triode connected (screen connected to plate).
:
:Now that I sort of understand this, I can now move on to some of the multitude of other things that puzzle me!
:Doug
::
::Hi Doug,
::
::I've emailed you Chapter 7 from THEORY AND APPLICATIONS of ELECTRON TUBES by Herbert J Reich, Ph.D. This chapter provides some good theory on Class A and Class AB1 power amplifiers. There is a good discussion on plate resistance / load.
::
::Gary
::
::
::
:::The recommended load resistance for an audio power triode is often 2 or 3 times the plate resistance. For example, here is data from an old (c. 1942) tube manual for single-ended power amps:
:::
:::2A3: plate res = 800 ohms, load = 2500 ohms
:::
:::45 @250V: plate = 1610, load = 3000
:::
:::6L6 (triode connected, fixed bias): plate = 1700, load = 5000
:::
:::Theoretically, the maximum power transfer to the speaker occurs when the plate resistance and load resistance are equal. In practice, however, there are other factors that change the equation - but I can't recall the explanation. Something to do with frequency response, perhaps?
:::
:::
We can change the grid bias just by changing the schematic to use a different cathode resistor or whatever form of bias is being used. All things are variable on paper. The optimum configuration is for the load resistance to be equal to approximately 2x plate resistance, the grid bias set for maximum allowable plate current, and a full swing of the peak grid signal, between -Vc/2 and +Vc/2 (Vc being the bias voltage). That combination will allow maximum power transfer to the speaker with minimum distortion.
(Of course, for a particular, real triode, it's not quite that simple because of non-linearities in the plate characteristic curves, etc. I guess that's why for a particular triode, the recommended load resistor isn't always 2x the plate resistance.)
Now, once an amp is built and running, and soldered up, then the die is pretty well cast. You can't easily "re-jigger" things - you just assume that the original designer optimized things.
Practically speaking, I would just look up the tube in the RCA manual, and use their recommended values for plate voltage, grid bias, load resistance, and cathode resistor, etc.
Doug
:
:Hi Doug,
:
:You got me thinking, what techniques are used to "re-jigger" the grid voltage?
:
:I believe Inverse Feedback is used, where a portion of the audio output is fed back to the grid to lower the source impedance of the circuit, reducing distortion. This is especially true when the load is a loudspeaker, where the load impedance varies with frequency.
:
:Gary
: