# Differential Amplifier with Capacitor

#### guitarpsycho182

Joined Jun 20, 2011
1

#### CraigHB

Joined Aug 12, 2011
127
When I run into this kind of thing, I usually go straight to SPICE. So much easier than doing analysis by hand and you can see things graphically with a mouse click. Unless, of course, you need to do it as a learning exercise.

I was recently working out a differential amplifier for a current sensing circuit myself. I just tried different values of capacitance in the simulator until I got the bandwidth where I needed it.

If you don't have ready access to a SPICE program, LTSPICE is free. I like it a lot and it does what I need to do.

#### t_n_k

Joined Mar 6, 2009
5,455
My guess is that if the op-amp is ideal a cap across the +/- input terminals would have no effect.

#### CraigHB

Joined Aug 12, 2011
127
For an ideal op-amp with no feedback, yes, a cap across the inputs would have minimal effect. However, putting a cap accross the inputs on a differential amp with reasonable gain acts as a low-pass filter. Useful if you need to filter out noise from something like a DC-DC converter.

#### t_n_k

Joined Mar 6, 2009
5,455
So if the OP wants to derive a mathematical s-domain representation then they would need to substitute the ideal op amp with a non-ideal op-amp model. As a start they could assume a finite gain with infinite bandwidth.

#### t_n_k

Joined Mar 6, 2009
5,455
Making the assumption about non-infinite gain (|Av|) but ideal op-amp properties in all other respects, I have the s-domain output voltage in terms of the differential inputs V1 and V2 as ...

$$V_o=-\frac{\frac{V_1 R_f}{R_1+R_f}-\frac{V_2R_g}{R_2+R_g}}{\frac{1}{A_v}+\frac{R_1}{R_1+R_f}\{ 1+\frac{R_fCs}{A_v} \}}$$

Needs checking but superficially looks OK.

One would imagine adding additional non-ideal properties would increase the analytical burden significantly. This is why CraigHB's suggestion of using simulation makes a lot of sense.

If all R's were the same value R & (2/Av)<<1 then the simplified result is ...

$$V_o=-\frac{V_1-V_2}{1+\frac{RCs}{A_v}}$$

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