1. Passive filters Use Passive components (R, L, C) Does not provide gain
Bulky inductors for low frequencies (not suitable
for integration)
RC filters cannot realize Q > 0.5
Filters parameters are coupled (changing one
component can change different filter parameters)
Cannot realize ideal integrator

2. Integrated Circuits

3. Chip micrograph
Wi-Fi Receiver
17mm2

4. Integrated Inductors Used in GHz range (L in the range of nH)
Low quality factor (need Q-enhancement)
Value of L (also R & C) not well controlled

5. Operational Amplifier Model: Basic
Represented by:
A= open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid = amplifier input resistance
Ro = amplifier output resistance
Signal developed at amplifier output is in phase with the voltage applied at + input (non-inverting) terminal and 1800 out of phase with that applied at - input (inverting) terminal.

6. Operational Amplifier Model: With Source and Load
RL = load resistance
RS = Thevenin equivalent resistance of signal source
vs = Thevenin equivalent voltage of signal source
and
Op amp circuits are mostly dc-coupled amplifiers. Signals vo and vs may have a dc component representing a dc shift of the input away from Q-point.
Op-amp amplifies both dc and ac components.

7. Problem: Calculate voltage gain
Given Data: A=100, Rid =100kW, Ro = 100W, RS =10kW, RL =1000W
Analysis:
Ideal amplifier’s output depends only on input voltage difference and not on source and load resistances. This can be achieved by using fully mismatched resistance condition (Rid >> RS or infinite Rid and Ro << RL or zero Ro ).
A = open-loop gain (maximum voltage gain available from the device)

8. Ideal Operational Amplifier
Ideal op amp is a special case of ideal differential amplifier with infinite gain, infinite Rid and zero Ro .
If A is infinite, vid is zero for any finite output voltage.
Infinite input resistance Rid forces input currents i+ and i- to be zero.
Ideal op amp has following assumptions:
Infinite common-mode rejection, power supply rejection, open-loop bandwidth, output voltage range, output current capability and slew rate
Zero output resistance, input-bias currents and offset current, input-offset voltage.

9. Inverting Amplifier: Configuration
Positive input is grounded.
Feedback network, resistors R1 and R2 connected between inverting input and signal source and amplifier output node respectively.

10. Inverting Amplifier:Voltage Gain
Negative voltage gain implies 1800 phase shift between dc/sinusoidal input and output signals.
Gain greater than 1 if R2 > R1
Gain less than 1 if R1 > R2
Inverting input of op amp is at ground potential (not connected directly to ground) and is said to be at virtual ground.
But is=i2 and v-=0 (since vid=v+-v-=0)
and

11. Non-inverting Amplifier: Configuration
Input signal is applied to the non-inverting input terminal.
Portion of the output signal is fed back to the negative input terminal.
Analysis is done by relating voltage at v1 to input voltage vs and output voltage vo .

12. Unity-gain Buffer
A special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Av =1.
Provides excellent impedance-level transformation while maintaining signal voltage level.
Ideal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage.
Unity-gain buffer is used in may sensor and data acquisition systems.

15. Alternative realization
Prone to parasitic capacitance
Voltage swing on the input terminals

17. Differentiator Since iR= is
Input resistor R1 in the inverting amplifier is replaced by capacitor C.
Derivative operation emphasizes high-frequency components of input signal, hence is less often used than the integrator.
Output is scaled version of derivative of input voltage.

19. Passive realization
Non-inverting realization

20. How to implement RHP zero?

21. All-pass filter

25. Low-pass Frequency Response
For Q=0.707,magnitude response is maximally flat (Butterworth Filter: Maximum bandwidth without peaking)
For Q>0.707, response shows undesired peaking.
For Q<0.707: Filter’s bandwidth capability is wasted.
At w<<wo, filter has unity gain.
At w>>wo response exhibits two-pole roll-off at -40dB/decade.
At w=wo, gain of filter =Q.

26. High-pass Frequency Response
For Q=0.707,magnitude response is maximally flat (Butterworth Filter response).
Amplifier gain is constant at w>wo, the lower cutoff frequency of the filter.

27. Band-pass Frequency Response
Response peaks approximately at wo.
At w<<wo or w>>wo, filter response corresponds to single-pole high-pass or low-pass filter changing at a rate of 20dB/decade.

28. Single amplifier Biquad (SAB)
Enhanced Positive Feedback (EPF)
Enhanced Negative Feedback (ENF)