Hi,
I recently analyzed the presence control found in this Marshall schematic. This probably won't be news to many, but the information on the web was not enough to completely convince me why it does exactly what it does. If anyone can confirm my analysis, that would be great!
At first glance, there is a voltage divider used as input to the long-tail pair. However, it seems like there could be significant loading as the feedback resistor is not orders lower than the plate resistors. I wasn't really clear on the impact of said loading, so there was some math.
[comment]\\$
Starting with affine approximation of the LTP's AC behavior:\\
$i_1 = k_1(v_{+} - Z_{t}(i_1+i_2) - v_t)$\\
$i_2 = k_2(v_{-} - Z_{t}(i_1+i_2) - v_t)$\\
where $Z_t$ is the tail resistance (plus the negligible bias resistance) and $v_t$ is the voltage below the tail.\\
\\
By KCL,\\
$\frac{v_f - v_t}{Z_f} - \frac{v_t}{Z_p} + i_1 + i_2 = 0 \implies v_t = \frac{v_f + (i_1+i_2)Z_f}{1 + \frac{Z_f}{Z_p}}$\\
where $v_f$ is the speaker voltage, $Z_f$ is the feedback impedance, and $Z_p$ is the presence control impedance.\\
\\
Letting $v_- = v_t$,\\
$i_1 = k_1(v_{+} - Z_{t}'(i_1+i_2) - \frac{v_f}{1 + \frac{Z_f}{Z_p}})$\\
$i_2 = k_2(-Z_{t}(i_1+i_2))$\\
where $Z_t' = Z_t + \frac{Z_f}{1+\frac{Z_f}{Z_p}}$.\\
\\
So long as $|Z_f| \gg |Z_p|$ and $Z_f \not\gg Z_t$, $Z_t' \approx Z_t$. It seems clear enough that small differences in $k_1$, $k_2$ and $Z_t$, $Z_t'$ lead only to small variations in amplitude and phase of $i_1$ and $i_2$ with respect to each other, rather than anything weird. [/comment]
In particular, in the only dependence, v_+ and the v_f term are directly summed. This seems to indicate that even if the tubes are behaving highly nonlinearly wrt Vgk, the feedback input is still doing its job. (And this confirms the intended behavior of subtracting from v_+ rather than adding to v_- in order to diminish the effect of imbalanced outputs of the LTP.)
I guess the important observation is that any variations in i_1+i_2 caused by variations in v_f are pretty small (unlike, say, variations in i_1-i_2), so that they do not interfere much with Z_p's ability to sense i_f.
As for the v_f term itself, here are some plots of it vs v_f:
For the pot settings, green is at 0, blue is 0.25, red is 0.5, cyan is 0.75, and purple is 1. Notably, there is still quite a lot of NFB even with presence maxed.
When designing a presence control, it seems useful to have a switch to disconnect R_f completely, in case NFB is not desired. Am I correct in thinking this is a good way to toggle it? (Shorting v_t seems like it would produce a pop.)
I recently analyzed the presence control found in this Marshall schematic. This probably won't be news to many, but the information on the web was not enough to completely convince me why it does exactly what it does. If anyone can confirm my analysis, that would be great!
At first glance, there is a voltage divider used as input to the long-tail pair. However, it seems like there could be significant loading as the feedback resistor is not orders lower than the plate resistors. I wasn't really clear on the impact of said loading, so there was some math.
[comment]\\$
Starting with affine approximation of the LTP's AC behavior:\\
$i_1 = k_1(v_{+} - Z_{t}(i_1+i_2) - v_t)$\\
$i_2 = k_2(v_{-} - Z_{t}(i_1+i_2) - v_t)$\\
where $Z_t$ is the tail resistance (plus the negligible bias resistance) and $v_t$ is the voltage below the tail.\\
\\
By KCL,\\
$\frac{v_f - v_t}{Z_f} - \frac{v_t}{Z_p} + i_1 + i_2 = 0 \implies v_t = \frac{v_f + (i_1+i_2)Z_f}{1 + \frac{Z_f}{Z_p}}$\\
where $v_f$ is the speaker voltage, $Z_f$ is the feedback impedance, and $Z_p$ is the presence control impedance.\\
\\
Letting $v_- = v_t$,\\
$i_1 = k_1(v_{+} - Z_{t}'(i_1+i_2) - \frac{v_f}{1 + \frac{Z_f}{Z_p}})$\\
$i_2 = k_2(-Z_{t}(i_1+i_2))$\\
where $Z_t' = Z_t + \frac{Z_f}{1+\frac{Z_f}{Z_p}}$.\\
\\
So long as $|Z_f| \gg |Z_p|$ and $Z_f \not\gg Z_t$, $Z_t' \approx Z_t$. It seems clear enough that small differences in $k_1$, $k_2$ and $Z_t$, $Z_t'$ lead only to small variations in amplitude and phase of $i_1$ and $i_2$ with respect to each other, rather than anything weird. [/comment]
In particular, in the only dependence, v_+ and the v_f term are directly summed. This seems to indicate that even if the tubes are behaving highly nonlinearly wrt Vgk, the feedback input is still doing its job. (And this confirms the intended behavior of subtracting from v_+ rather than adding to v_- in order to diminish the effect of imbalanced outputs of the LTP.)
I guess the important observation is that any variations in i_1+i_2 caused by variations in v_f are pretty small (unlike, say, variations in i_1-i_2), so that they do not interfere much with Z_p's ability to sense i_f.
As for the v_f term itself, here are some plots of it vs v_f:
For the pot settings, green is at 0, blue is 0.25, red is 0.5, cyan is 0.75, and purple is 1. Notably, there is still quite a lot of NFB even with presence maxed.
When designing a presence control, it seems useful to have a switch to disconnect R_f completely, in case NFB is not desired. Am I correct in thinking this is a good way to toggle it? (Shorting v_t seems like it would produce a pop.)
Thanks for the painstaking analysis.
It might be noted that this plan comes from Fender 5F6a.
The high-ish NFB network impedance should not be a big problem. The 10K tail resistor gets current from two tubes working anti-phase. Its current is nearly constant, so looking "up" into the tail should be a fairly high resistance. This is shunted by grid networks but they too are high impedance.
And the ~~4.2K impedance is a practical compromise. Pots smaller than 5K are less common. And at the time, caps larger than 0.1u were more expensive, being 200V film at least. Electrolytics started at a couple uFd with very wide tolerances and large drift in low-volt products. 5K+0.1u is a happy balance between the circuit need for fairly low impedance and commercially available parts.
A comment: the long-tail was known long before Fender. But "obviously" the 10K tail resistor should go to ground, and the 0.1u grid-cap to the NFB network. It might be speculated that 10K tail to the NFB is a wiring mistake. However it not only persisted but was widely copied. I think it "adds something" useful to guitarists. My guess is 2nd harmonic, but I have been too lazy to check this or how it might vary with frequency.
It might be noted that this plan comes from Fender 5F6a.
The high-ish NFB network impedance should not be a big problem. The 10K tail resistor gets current from two tubes working anti-phase. Its current is nearly constant, so looking "up" into the tail should be a fairly high resistance. This is shunted by grid networks but they too are high impedance.
And the ~~4.2K impedance is a practical compromise. Pots smaller than 5K are less common. And at the time, caps larger than 0.1u were more expensive, being 200V film at least. Electrolytics started at a couple uFd with very wide tolerances and large drift in low-volt products. 5K+0.1u is a happy balance between the circuit need for fairly low impedance and commercially available parts.
A comment: the long-tail was known long before Fender. But "obviously" the 10K tail resistor should go to ground, and the 0.1u grid-cap to the NFB network. It might be speculated that 10K tail to the NFB is a wiring mistake. However it not only persisted but was widely copied. I think it "adds something" useful to guitarists. My guess is 2nd harmonic, but I have been too lazy to check this or how it might vary with frequency.
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I would be interested to hear more about the 2nd harmonic theory. It's not really obvious to me why it would happen.
All I can think of are: a) slightly more NFB due to the NFB being "seen" by the non-inverting input, which has slightly more gain if the valves and plate resistors are equal and b) both slightly less differential gain and non-differential gain, independent of NFB, due to the Z' impedance being present in the system of equations above. I would think both these lead to less 2nd harmonic distortion, although probably negligibly so (although if the plate resistors were unequal, I could see a) leading to less NFB / more distortion). What else am I missing?
All I can think of are: a) slightly more NFB due to the NFB being "seen" by the non-inverting input, which has slightly more gain if the valves and plate resistors are equal and b) both slightly less differential gain and non-differential gain, independent of NFB, due to the Z' impedance being present in the system of equations above. I would think both these lead to less 2nd harmonic distortion, although probably negligibly so (although if the plate resistors were unequal, I could see a) leading to less NFB / more distortion). What else am I missing?
Find the answer here : The Long-Tail Pair.
The feedback signal goes to two inputs rather than one (the tail resistor's bottom end is a third input, which is common-mode) in order to compensate for the inherent gain difference between halves which is even increased by the different plate resistor values... and these different values have been introduced for the same reason, just this time to balance out the gain of the sections for the main signal input.
So, it's all on purpose, in order to get well balanced outputs for both main and feedback signals.
The feedback signal goes to two inputs rather than one (the tail resistor's bottom end is a third input, which is common-mode) in order to compensate for the inherent gain difference between halves which is even increased by the different plate resistor values... and these different values have been introduced for the same reason, just this time to balance out the gain of the sections for the main signal input.
So, it's all on purpose, in order to get well balanced outputs for both main and feedback signals.
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