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

2. 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

3. 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

4. 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

5. 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

6. Basics of OP AMP-RC Circuits
Weighted summer
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Basics of OP AMP-RC Circuits

7. 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

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

9. 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

10. 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

11. 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

12. Inverting lossy integrator
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Basics of OP AMP-RC Circuits

13. Inverting weighted summing integrator
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Basics of OP AMP-RC Circuits

14. Basics of OP AMP-RC Circuits
Subtractor
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Basics of OP AMP-RC Circuits

15. 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

16. 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

17. Inverting first-order section
inverting lossing integrator
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Basics of OP AMP-RC Circuits

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

19. 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
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Basics of OP AMP-RC Circuits

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

21. 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

22. 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

23. 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

24. RC-CR transformation (2)
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Basics of OP AMP-RC Circuits

25. 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

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