Hey, so I've probably beaten the preamp threads dead but I was curious about how the math checked out for the frequency response of this MPF102 (credit: James Hawes) take on the Tillman preamp. I wired it up and sounds great, but wanted to see how the response looked on paper.
Using the AC model for the JFET:
Where:
RL = R4 (in parallel with load resistance)
RD = R2
RS = R3
C = C1
Plotting this shows that it appears as a normal high pass filter, but I wanted to figure out the equation for the -3db frequency:
\(
\frac{V_{o}}{V_{i}} = [\frac{-g_{m}R_{D}}{1 + g_{m}R_{S}}][\frac{sR_{L}C}{1 + s(R_{L} + R_{D})C}]
\)
The conclusion was that while solving for the -3dB frequency, there was a range of load resistances 'RL' that would result in a negative/zero denominator under the square root which doesn't make sense to me.
Using the resistor values given in the original design I calculated that RL would have to be larger than around 3.5 Kohm for the calculation of f3dB to have a valid denominator under the root. With this in mind, I plotted the magnitude of the frequency response with a resistor within this 'unaccepted range' and it showed to be normal...
I am stumped. I don't know why the math doesn't check out... Any ideas?
Thanks,
JP
Using the AC model for the JFET:
Where:
RL = R4 (in parallel with load resistance)
RD = R2
RS = R3
C = C1
Plotting this shows that it appears as a normal high pass filter, but I wanted to figure out the equation for the -3db frequency:
\(
\frac{V_{o}}{V_{i}} = [\frac{-g_{m}R_{D}}{1 + g_{m}R_{S}}][\frac{sR_{L}C}{1 + s(R_{L} + R_{D})C}]
\)
The conclusion was that while solving for the -3dB frequency, there was a range of load resistances 'RL' that would result in a negative/zero denominator under the square root which doesn't make sense to me.
Using the resistor values given in the original design I calculated that RL would have to be larger than around 3.5 Kohm for the calculation of f3dB to have a valid denominator under the root. With this in mind, I plotted the magnitude of the frequency response with a resistor within this 'unaccepted range' and it showed to be normal...
I am stumped. I don't know why the math doesn't check out... Any ideas?
Thanks,
JP
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