Analog Filters: Basics of OP AMP-RC Circuits Stefano Gregori The University of Texas at Dallas

Basics of OP AMP-RC Circuits Introduction So far we have considered the theory and basic methods of realizing filters that use passive elements (inductors and capacitors) Another type of filters, the active filters, are in very common use They were originally motivated by the desire to realize inductorless filters, because of the three passive RLC elements the inductor is the most non-ideal one (especially for low-frequency applications of filters in which inductors are too costly or bulky) When low-cost, low-voltage solid-state devices became available, active filters became applicable over a much wider frequency range and competitive with passive ones Now both types of filters have their appropriate applications Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Active-RC filters In this lesson we concentrate on active-RC filters. They make use of active devices as well as RC components. Active filters are usually designed without regard to the load or source impedance; the terminating impedance may not affect the performance of the filter it is possible to interconnect simple standard blocks to form complicated filters are noisy, have limited dynamic ranges and are prone to instability can be fabricated by integrated circuits Passive filters the terminating impedance is an integral part of the filter: this is a restriction on the synthesis procedure and reduces the number of possible circuits are less sensitive to element value variations are generally produced in discrete or hybrid form Stefano Gregori Basics of OP AMP-RC Circuits

Operational Amplifier symbol equivalent circuit In an ideal op-amp we assume: input resistance Ri approaches infinity, thus i1 = 0 output resistance Ro approaches zero amplifier gain A approaches infinity Stefano Gregori Basics of OP AMP-RC Circuits

Inverting voltage amplifier Example: vin(t) given R1 = 1 kΩ R2 = 2 kΩ V0 = 1 V f = 1 MHz vout(t) we have Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Weighted summer Stefano Gregori Basics of OP AMP-RC Circuits

Noninverting voltage amplifier Example: vin(t) given R1 = 1 kΩ R2 = 1 kΩ V0 = 1 V f = 1 MHz vout(t) we have Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Buffer amplifier Stefano Gregori Basics of OP AMP-RC Circuits

Inverting or Miller integrator R = 1 kΩ C = 1 nF V0 = 1 V f = 1 MHz Example: vin(t) given vout(t) we have Stefano Gregori Basics of OP AMP-RC Circuits

Inverting differentiator (1) Example: given R = 1 kΩ C = 100 pF V0 = 1 V f = 1 MHz vin(t) vout(t) we have Stefano Gregori Basics of OP AMP-RC Circuits

Inverting differentiator (2) R = 22 kΩ C = 47 pF vin(t) is a triangular waveform with: - vin max 2 V - vin min 0 V - frequency 500 kHz vin(t) vout(t) is a square waveform with: - vout max 2,068 V - vout min -2,068 V - frequency 500 kHz vout(t) Stefano Gregori Basics of OP AMP-RC Circuits

Inverting lossy integrator Stefano Gregori Basics of OP AMP-RC Circuits

Inverting weighted summing integrator Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Subtractor Stefano Gregori Basics of OP AMP-RC Circuits

Integrator and differentiator frequency behavior integrator integrator differentiator differentiator vin(t) is a sinewave with frequency f. Figure shows how circuit gain AV changes with the frequency f AV is the ratio between the amplitude of the output sinewave vout(t) and the amplitude of the input sinewave vin(t) R = 1 kΩ C = 1 nF Stefano Gregori Basics of OP AMP-RC Circuits

Low-pass and high-pass circuits low-pass circuit frequency behavior low-pass high-pass high-pass circuit R = 1 kΩ C = 1 nF Stefano Gregori Basics of OP AMP-RC Circuits

Inverting first-order section inverting lossing integrator Stefano Gregori Basics of OP AMP-RC Circuits

Noninverting first-order section noninverting lossing integrator Stefano Gregori Basics of OP AMP-RC Circuits

Finite-gain single op-amp configuration Many second-order or biquadratic filter circuits use a combination of a grounded RC threeport and an op-amp Stefano Gregori Basics of OP AMP-RC Circuits

Infinite-gain single op-amp configuration Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Gain reduction To reduce the gain to α times its original value (α < 1) we make and solving for Z1 and Z2, we get and Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Gain enhancement A simple scheme is to increase the amplifier gain and decrease the feedback of the same amount Stefano Gregori Basics of OP AMP-RC Circuits

RC-CR transformation (1) is applicable to a network N that contains resistors, capacitors, and dimensionless controlled sources conductance of Gi [S] → capacitance of Gi [F] capacitance of Cj [F] → conductance of Cj [S] the corresponding network functions with the dimension of the impedance must satisfy the corresponding network functions with the dimension of the admittance must satisfy the corresponding network functions that are dimensionless must satisfy Stefano Gregori Basics of OP AMP-RC Circuits

RC-CR transformation (2) Stefano Gregori Basics of OP AMP-RC Circuits

Basics of OP AMP-RC Circuits Sallen-Key filters lowpass filter frequency behavior lowpass highpass bandpass highpass filter R = 1 kΩ C = 1 nF Stefano Gregori Basics of OP AMP-RC Circuits

Types of biquadratic filters lowpass highpass bandpass bandreject allpass Stefano Gregori Basics of OP AMP-RC Circuits