Page 355 - Op Amps Design, Applications, and Troubleshooting

Differentiator 333

We can now compute Q with Equation (7.19) as

Let us plan to use a standard 0.05-microfarad capacitor for Q.

Compute 8|. Resistor RI should equal the reactance of Q at a frequency higher
than the normal operating frequency. In this way, R l has minimal effect for the
normal input signal but becomes effective for higher frequencies (noise). We can
compute a reasonable value for R x with Equation (7.20).

where f UG is the unity gain frequency of the op amp. For the present application,
we can compute the value of Rj as follows.

We will use the nearest standard value of 270 ohms.

Compute & 3. Resistor R 3 is always equal to R 2 in order to maintain equal IX
resistances in both of the op amp input terminals. Therefore, R 3 will also be a 12-
kilohm resistor.

Compute C 3. The reactance of capacitor C 3 should be less than one-tenth the
resistance of R 3 at a frequency that causes the reactance of Q to be equal to the
resistance of R 2. This ensures that resistor R 3 will be effectively bypassed for all
usable circuit frequencies. Since R 2 - R 3, we can express this in equation form as

In our present circuit, we require a value of

We wiE use a standard value of 0.47 microfarad for C 3.

Compute C%, In order to reduce the gain at high-noise frequencies and yet min-
imize the effect on normal circuit frequencies, we want to select capacitor C 2 such
that its reactance is equal to R 2 at a frequency well above the highest normal oper-