2: Lecture Simple Amplifier Review
Amplifier Gain and DC bias Amplifier Models STC circuits Amplifier frequency response
Amplifier
Amplifier Circuit Symbol
To amplify means to multiply by constant
Vo=Av x Vi Av is the gain Vo cannot increase indefinitely
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Amplifier with supply rails
To explicitly show the supply voltages, VCC and VEE are shown. In some cases, VEE is zero.
Linear and non-linear regions of operation
Amplifier Gain and DC Bias
Vi(t)=VI+vi(t)
Total instantaneous signal DC bias
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Amplifier Gain
Voltage Gain: Av = Vo VI (dB) 20log Av dB i Current Gain : Ai = o iI (dB) 20log Ai dB Power Gain: Ap =Av AI (dB) 10log ApdB
Note: multiplication of two numbers is equivalent to adding their logarithms
AP (dB )
1 AV (dB) AI (dB) 2
A few words about dB
When is the Gain in dB a negative number?
Inverting amplifier (180 degrees phase difference between input and output) Or when the amplifier is attenuating
dB is unitless:
20log (V/V) or 20log (I/I) or 10log(W/W)
Find the log of 0.1, 1, 10 , 100
-10dB, 0dB, 20dB, 40dB
If the gain is -6dB, what is the gain in V/V?
-6dB=20log(x) -> x=10-6/20 = 0.5
If gain is -3dB, what is the gain in V/V?
-6dB=20log(x) -> x=10-3/20 = 0.707 (i.e. 3 dB BW, Half Power). Why? 0.7072 = 0.5 Power = 10 log (p), Voltage = 20 log (v) but power prop to voltage squared.
Addition in dB is multiplication of term inside ():
40dB + 6dB = 46dB = 100x2=200
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Amplifier Models
Voltage Amplifier Current Amplifier Transconductance Amplifier Tranresistance Amplifier
1. Voltage Amplifier
Voltage controlled voltage source (VCVS)
Av = open circuit voltage gain
o
Vo Vi
V V io 0
Ri= input resistor Ro= output resistor
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With Signal and Load
Ri Vi Vs Ri Rs
Vo Avo Vi
RL RL Ro
Find overall Gain
Ri high, Ro low Unity Gain Av = 1
o
Ri RL Vo Av Ri Rs R L Ro Vs
o
Voltage Buffer Amp
2. Current Amplifier Model
current controlled current source (CCCS)
Ais = Short Circuit Current Gain
io ii A A Vo 0
Current Buffer Amp
Ri low, Ro high Unity gain, Ais = 1
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3. Transconductance Amp Model
voltage controlled current source (VCCS)
Gm = Short Circuit Transconductance
io Vi A V Vo 0
4. Transresistance Amp Model
current controlled voltage source (VCVS)
Rm = Open Circuit Transresistance
Vo ii V A io 0
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High Frequency Roll-off of an Amplifier
As frequency of operation increases, the gain of amplifier decreases. This chapter analyzes this problem.
Example: Human Voice I
Natural Voice
Telephone System
Natural human voice spans a frequency range from 20Hz to 20KHz, however conventional telephone system passes frequencies from 400Hz to 3.5KHz. Therefore phone differs conversation from face-to-face conversation.
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Example: Human Voice II
Path traveled by the human voice to the voice recorder
Mouth Air Recorder
Path traveled by the human voice to the human ear
Mouth Air Ear
Skull
Since the paths are different, the results will also be different.
Example: Video Signal
High Bandwidth
Low Bandwidth
Video signals without sufficient bandwidth become fuzzy as they fail to abruptly change the contrast of pictures from complete white into complete black.
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Frequency Response of Amplifiers
Frequency Response of Amplifiers
Assumptions: Linear amplifier Small signal analysis Given: Sinusoidal input
vi (t ) Vi sin t
Output is:
VO (t ) VO sin(t )
Ref. Sedra and Smith, Figure 1.20
Amplifier frequency response:
Amp bandwidth: band of frequencies over which gain is almost constant (typically 3dB) 1 to 2
Ref. Sedra and Smith, Figure 1.21
Frequency Response Analysis
Review of Single Time-Constant Networks
Circuits that can be reduced to one reactive component (capacitance or inductance) and one resistive component
Low Pass Filter
High Pass Filter
Ref. Sedra and Smith, Figure 1.22
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Find Magnitude and Phase
Voltage Amplifier with Input Ci
Example: Effect of input capacitance
A V0Vi
Find the amplifier voltage transfer function, DC gain, and high frequency roll-off.
Ref. Sedra and Smith, Figure 1.25
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Analysis
Voltage divider at input
Vi ( s )
Voltage divider at output
Vo ( s )
Overall amplifier transfer function
T (s) Vo ( s ) Vi ( s )
Frequency Response
Example 1.5
Rs 20k , Ri 100k , Ci 60 pF A V0 V 144 , Ro 200, RL 1k V
0 -10 -20
DC gain: 1 1 K A V0 R R 1 o 1 s RL Ri
-30
0.1
1
10
Direct-coupled
High frequency rolloff:
0
1
1 Ci RS // Ri
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Gain Roll-off: Common Source
The capacitive load, CL, is the culprit for gain roll-off since at high frequency, it will steal away some signal current and shunt it to ground. At low frequency, the capacitor is effectively open and the gain is flat. As frequency increases, the capacitor tends to a short and the gain starts to decrease. A special frequency is =1/(RDCL), where the gain drops by 3dB.
1 Vout g mVin RD || CL s
Identify the poles
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Identify the poles
Relationship between Frequency Response and Step Response The relationship is such that as R1C1 increases, the bandwidth drops and the step response becomes slower.
H s j
t Vout t V0 1 exp u t R1C1 R12C12 2 1
1
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Examples: Amplifier Frequency Response
Capacitively coupled ac-amplifier
Lower Corner
Direct-coupled dc-amplifier
Upper Corner
Tuned or bandpass amplifier
Ref. Sedra and Smith, Figure 1.26
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