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Circuit computes first derivative

-December 31, 1969

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

 

where REQ 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 VOUT –REQ C1 sVIN for input frequencies lower than 1/2pREQ C1 . If R3 is much greater than the parallel combination of R1 and R2 , then REQ R3 . On the other hand, if R3 is set at 0W, 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, VN in the classic inverting differentiator, produces output noise of magnitude RCsVN . In the case of the differentiator in Figure 1, the equivalent input noise produces an output magnitude of only (1+R2 /R1 )VN . (DI #2522)

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