Circuit computes first derivative

The circuit in Figure 1 computes the derivative of an input signal as the integral of the input signal minus the signal itself.

Figure 1.	This circuit produces less noise than the classic inverting differentiator.

The response of the circuit is

where R_EQ is the parallel equivalent resistance of R₁ and R₂ plus the resistance of R₃, or

This response is identical to that of the classic inverting differentiator, in which the response is

for input frequencies lower than

If R₃ is much greater than the parallel combination of R₁ and R₂, then R_EQ ≈ R₃. On the other hand, if R₃ is set at 0 Ω, the bias currents of the op amp balance to minimize voltage offsets, and

A major problem with the classic inverting differentiator is high noise. By its nature, a differentiator must exhibit increasing gain with frequency, and this increasing gain amplifies the inherent amplifier noise. An equivalent input-noise voltage, V_N in the classic inverting differentiator, produces output noise of magnitude RCsV_N. In the case of the differentiator in Figure 1, the equivalent input noise produces an output magnitude of only