How to find the transfer function of this volume control?

[davidel94]

what is the transfer function of this circuit? R3 and R4 are a potentiometer divided into two resistors.

 

[richie00boy]

R4 is providing in effect negative feedback, because in the loop is an inverting amplifier.

 

[willysan]

Let's say Vi is the input voltage and Vo the output voltage. Let's pray my knowledge of circuit theory is OK.
In such a case: Vo/Vi=-R4/{[R1/(1/R2+jwC2)](1/R5+1/R4+1/R3)-1/R3}

 

[davidel94]

i've simulated your transfer function and it is not right because it should give with the values in the photo -2.63dB which is a gain of 0.738 V/V, with your formula i have a gain of about 13 V/V

 

[DF96]

The title asks how to find the function. The text ask what it is. I will answer the first question. Circuit theory plus some algebra.

 

[davidel94]

i now what a transfer function is but i don't know how to calculate the transfer function of this circuit

 

[DF96]

Where did you find the circuit? What is your application? Please assure us that this is not a student assignment.

 

[djoffe]

this is a variant of the Douglas Self/Baxandall high level gain stage circuit. It does a fairly good approximation of log gain with a linear pot. He uses essentially this in his latest preamp.

Akitika GT-101

Update My Dynaco

 

[willysan]

The first time I derived the transfer function in a hurry. I checked it later and found a mistake.
Now it's my turn to ask. How did you know the mid-frequency gain was -2.63 dB?

 

[davidel94]

i simulated it with LTspice but yesterday i calculated by myself the transfer function so now i have it and i don't need your help. thanks anyway

 

[DF96]

Perhaps in the spirit of DIY you could share it with us?

 

[glennb]

Let Vs be the voltage at the R3,4,5 summing junction

Inverter gain:
Vo = -R2/R1 * Vs

Zero sum of currents at Vs:
0= (0-Vs)/R5 + (Vi-Vs)/R4 + (Vo-Vs)/R3

Ignoring the capacitor, solving and rearranging, the transfer function is:

Vo/Vi = -1 / ( R4 * [ R1 * R2 * ( 1/R4 + 1/R5 +1/R3 ) + 1/R3 ] )

This gives Vo/Vi = -0.7379389 for the resistor values above.

QED

 

[davidel94]

in this circuit i considered the gain of the op.amp to be equal to 1, so v1=vout, then i calculated vs using the voltage divider rule which gives:
vs= v1*(R8/(R8+((R2*(R7+R10))/(R2+R7+R10))))
then i wrote a node equation in v1
(vin-v1)sC4-v1/R1-(v1-vs)/R2=0
considering v1=vout i substituted for vs in the second equation which gives:
vout/vin=-C4 s/(-C4 s+(-1+R8/(R2 (R7+R10)/(R2+R7+R10)+R8))/R2-1/R1)
then i calculated the magnitude which gives:
|vout/vin|=C4 w/(sqrt ((-C4 w)^2+((-1+R8/(R2 (R7+R10)/(R2+R7+R10)+R8))/R2-1/R1)^2))
ltspice gives a -3dB point at 3.140kHz.
where is my mistake?

 

[JMFahey]

Please answer about your first circuit before asking for a second, unrelated one in the same post.
Thanks.