math question about frequency cut with collector-to-base capacitors

[Derringer]

so lets say there is a gain stage like this
R1 =390K
R2 =100K
R3 = 10K
R4 = 2K7
C1 = 0.1uf
C2 = 10uF
Vcc is 9V, ground is Zero volts

If a capacitor of 1000 pF is connected between the base and collector of the transistor to create a lowpass filter, how do you find the corner frequency and how steep is the rolloff curve?


if it matters, lets say that this circuit is being driven by a 2n5457 buffer (3k3 source resistor) and then this npn gain stage leads to a 0.1 uf Cap into a 100K volume pot.

[Kesh]

Wiki Miller effect.

Basically your cap has a effective value of (Av + 1) multiplied by its actual value, where Av is the voltage gain of your circuit.

And will act as if it's going from base to ground.

Voltage gain is R3/ Ree, where Ree is the internal emitter resistance. Ree will be tiny so gain is going to be at the limit of the power supply and will clip.

Not sure how Miller effect works with clipping. I'd imagine use the actual gain, not the R3/Ree, which is determined by the power rails.

[Jazznoise]

Not be rude but we just had a thread on this!

[Derringer]

Not be rude but we just had a thread on this!

sorry .... link please?

and thanks guys


looking at Aiken's site right now
http://www.aikenamps.com/MillerCapacitance.html

Effect on frequency response

   The input capacitance of the tube, in conjunction with the source impedance of the previous stage, forms a simple, single-pole RC lowpass filter with a -6dB/octave (-20dB/decade) slope, and an  upper -3dB cutoff frequency equal to:

       f = 1/(2*pi*R*C)

   The -3dB point with a 68K resistor (such as at the input stage of an amplifier) would be:

       f = 1/(2*pi*68K*151.1pF) = 15.5kHz

so is the source impedance in the above example equal to the parallel value of R1 and R2 + whatever small amount is coming from the previous buffer = @ 80K ?

[Jazznoise]

http://www.diystompboxes.com/smfforum/index.php?topic=98989.0

[Kesh]

that thread doesn't cover collector to base caps

[Derringer]

can anyone confirm what I'm looking at from Aiken as correct?

[amptramp]

I get the cutoff to be 15497.7 Hz for the example in Aiken.  That's as close as whoremonger is to swearing.  His write-up seems to be correct.

Miller capacitance is fairly simple to understand:  In the example with a gain of 61, if you reduce the input by 1 millivolt, the plate voltage goes up by 61 millivolts.  Since the plate is going in the opposite direction of the grid, the voltage difference between capacitor electrodes will add.  The current through the capacitor will depend on the voltage across it, so it will see a change of 62 millivolts, giving the same effect as a grid-to-ground capacitor 62 times the value of the grid-to-plate Miller capacitance.

Transistors have a capacitance that varies with collector-to-base voltage, getting lower as the difference gets higher, whereas tube interelectrode capacitances are much smaller and have little variation with operating point.  Some transistors have capacitance vs. Vcb in their spec sheets.  It does explain why some transistor feedback circuits oscillate at certain points in the waveform but not others.  Aiken's suggestion of going to a cascode topology works well with transistors.

[Derringer]

thanks amptrap

but more specifically, in this example

so lets say there is a gain stage like this
R1 =390K
R2 =100K
R3 = 10K
R4 = 2K7
C1 = 0.1uf
C2 = 10uF
Vcc is 9V, ground is Zero volts

If a capacitor of 1000 pF is connected between the base and collector of the transistor to create a lowpass filter, how do you find the corner frequency and how steep is the rolloff curve?


if it matters, lets say that this circuit is being driven by a 2n5457 buffer (3k3 source resistor) and then this npn gain stage leads to a 0.1 uf Cap into a 100K volume pot.

390K || 100K = @80K
I'm not sure what the output impedance of a mid-rail biased 2n5457 buffer with a 3k3 source resistor is, but I assume it's low and negligible for this scenario.

so then a 1000pf cap between the Qbase and Qcollector along with the 390K/100K biasing network would create a lowpass filter with a -6dB/octave (-20dB/decade) slope, and an  upper -3dB cutoff frequency at about 2KHz

am I applying things to this transistor design correctly

[DougH]

that thread doesn't cover collector to base caps

If C2 is big enough you can assume base is at ground as far as the collector-base cap is concerned.

[Jazznoise]

Also, we covered impedance! My point was that the question could be added in the other thread or deduction could be used. Having one nice thread with lots of points well discussed is much more useful than a million threads with a good post in each one!