Transcript UniMasr.com_109

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
Integrated Circuits
Chip micrograph
Wi-Fi Receiver
17mm2
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
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.
Operational Amplifier Model: With
Source and Load
RL = load resistance
RS = Thevenin equivalent
resistance of signal source
vs = Thevenin equivalent voltage
of signal source
R
R
L
and vid  vs R id
vo*  Av
R
id Ro  R
id S
L
R
R
id
L
Av 

vs Rid  RS Ro  RL
vo
•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.
Problem: Calculate voltage gain
Given Data: A=100, Rid =100kW, Ro = 100W, RS =10kW, RL =1000W
Analysis:
R
R
vo
id
L
Av 

vs Rid  RS Ro  RL



100kW
1000W



 100

  82.6  38.3dB


 10kW 100kW  100W 1000W 
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 ).
vo  Av
id
Av 
vo
v
A
id
A = open-loop gain (maximum voltage gain available from the device)
Ideal Operational Amplifier
Ideal op amp is a special case of ideal differential amplifier with infinite
gain, infinite Rid and zero Ro .
v
v  o
id A
lim vid  0
A 
 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, inputoffset voltage.
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.
Inverting Amplifier:Voltage Gain
vs  isR  i R  vo  0
1 2 2
But is=i2 and v-=0 (since vid=v+-v-=0)
R
vs
vo
is 
 2
and Av 
R
vs
R
1
1
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
.
Non-inverting Amplifier: Configuration
R R
vo  vs 1 2
R
1
R
v o R1  R2
 Av 

 1 2
R
vs
R
1
1
• 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 .
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.
Alternative realization
 Prone to parasitic capacitance
 Voltage swing on the input terminals
Differentiator
v
i  o
R
R
dvs
is  C
dt
Since iR= is
dvs
vo  RC
dt
• 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.
Passive realization
R
1 sC R
2
11
Av (s) 

.
.
R

R
1 s(R // R )(C  C )
v
1
2
1 2 1 2
in
vo
Non-inverting realization
R  R 1 s(R // R )(C  C )
1 2 1 2 .
Av (s) 
 1 2.
R
1 sC R
v
2
11
in
vo
How to implement RHP zero?
R 1 sC R
1 1.
Av (s) 
 2
R 1 sC R
v
2 2
1
in
vo
All-pass filter
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.
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.
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.
Single amplifier Biquad (SAB)
Enhanced Positive Feedback (EPF)
Enhanced Negative Feedback (ENF)