Passive filters Use Passive components (R, L, C) Does not provide gain Bulky inductors for low...
-
Upload
may-wilson -
Category
Documents
-
view
215 -
download
1
Transcript of Passive filters Use Passive components (R, L, C) Does not provide gain Bulky inductors for low...
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 Receiver17mm2
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 resistanceRS = Thevenin equivalent resistance of signal source
vs = Thevenin equivalent voltage of signal source
LRoRLRA
idv*
ov
•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.
LRoRLR
SR
idRidR
vA svov
SR
idRidR
svidvand
Problem: Calculate voltage gain
Given Data: A=100, Rid =100k, Ro = 100, RS =10k, RL =1000Analysis:
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)
dB3.386.820100100
1000k100k10
k100100
svov
LRoRLR
SR
idRidR
vA
idvov A AvA
idvov
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.
Aov
idv 0
idvlim
A
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
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.
0ov22i
1isv RRs
1
svsi R
But is=i2 and v-=0 (since vid=v+-v-=0)
and
1
2
svov
R
RvA
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 .
1
21121
svov121
svov
R
R
RRR
vA
RRR
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
• 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.
Rov
Ri dtsdvCsi
Since iR= is
dtsdvRCov
Output is scaled version of derivative of input voltage.
.11
1
)21
)(2
//1
(1.
2
21
invov)(
RsC
CCRRs
R
RRsvA
Passive realization
Non-inverting realization
.)21
)(2
//1
(111
1.21
2
invov)(
CCRRs
RsC
RR
RsvA
How to implement RHP zero?
.22
111
1
1
2
invov)(
RsC
RsC
R
RsvA
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 <<o, filter has unity gain.At >>o response exhibits two-pole roll-off at -40dB/decade.At =o, 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 >o, the lower cutoff frequency of the filter.
Band-pass Frequency Response
Response peaks approximately at o.
At <<o or >>o, 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)