Figure 1 Electrical Amplifier.
Figure 2 Input Waveform.
Lecture Notes: 2304154 Physics and Electronics
Lecture 8 (2nd Half), Year: 2007
Physics Department, Faculty of Science, Chulalongkorn University
15/11/2007
Contents
1 Operational Amplifiers
4
2 Problems
9
Amplifier
Amplifier : The circuit ideally produces an output signal with identical waveshape
as the input signal, but with a larger amplitude.
Noninverting and Inverting Amplifier (in Figure 2, 3, and 4 )
Input and Output Resistance
Ri = input resistance (impedance)
Ro = output resistance (impedance)
Avoc = open–circuit voltage gain (no RL )
2304154 Physics and Electronics (file: lec08 2.tex)
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Figure 3 Noninverting output waveform.
Figure 4 Inverting output waveform.
Figure 5 Model of an electronic amplifier.
2304154 Physics and Electronics (file: lec08 2.tex)
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Figure 6 Circuit for Example 1.
Gain of Amplifier
Voltage Gain:
Av =
vo
vi
Current Gain:
io
ii
vo /RL
Ri
=
= Av
vi /Ri
RL
Ai =
Av < Avoc because of voltage drop across Ro
Power Gain:
Po
Pi
Vo Io
Ri
=
= Av Ai = (Av )2
Vi Ii
RL
G=
Example 1. (Fig. 6) Find Avs = Vo /Vs and Av = Vo /Vi
Ri
Vs = 0.667 mV
R i + Rs
Avoc Vi = 104 Vi = 6.67 V
RL
= 5.33 V rms
Vo = Avoc Vi
RL + Ro
Vi =
Vo
= 8000
Vi
Vo
=
= 5333
Vs
Av =
Avs
2304154 Physics and Electronics (file: lec08 2.tex)
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Figure 7 Rin >> Rs .
Figure 8 Rin << Rs .
Importance of Input Impedance (Fig. 7 and 8)
If Rin >> Rs , then vin ∼
= vs . Ex: Voltage mesurement of electrodes on the person’s
skin. If Rin << Rs , then iin ∼
= is . Ex: Ammeter.
Importance of Output Impedance
• Low output impedance: for variable resistance load (series of loundspeakers)
• High output impedance: for load need a constant current (light of LED)
Ideal Amplifiers
• Voltage amplifier: Ri = ∞;
Ro = 0;
Gain Parameter Avoc
• Current amplifier: Ri = 0;
Ro = ∞;
Gain Parameter Aisc
• Transconductance amplifier: Ri = ∞;
• Transresistance amplifier: Ri = 0;
1
Ro = ∞;
Ro = 0;
Gain Parameter Gmsc
Gain Parameter Rmoc
Operational Amplifiers
Symbol of Op-Am (in Figure 9)
V1 (+) = noninverting input
V2 (−) = inverting input
IC(LM741) of Op-Am (in Figure 10 and 11)
2304154 Physics and Electronics (file: lec08 2.tex)
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Figure 9 The symbol of op–am.
Figure 10 The IC LM741 of op–am.
Figure 11 The IC LM741 of op–am.
2304154 Physics and Electronics (file: lec08 2.tex)
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Figure 12 Inverting amplifier.
Virtual Ground
Because Iin ≈ 0
V1 ≈2
Inverting Amplifier (in Figure 12)
Given I1 on R1 and I2 on R2 : KCL & Ohm’s Law
Visual Ground: Vs ≈ Vin = 0
I1 + I2 = 0
VS − Vin
I1 =
R1
VS − Vout
I2 =
R2
R2
Vout
=−
AV =
Vin
R1
Noninverting Amplifier (in Figure 13)
Visual Ground:
Given I1 on R1 and I2 on R2 : KCL & Ohm’s Law
I1 + I2 = 0
Vin
I1 =
R1
Vout − Vin
I2 =
R2
Vout
R2
AV =
=1+
Vin
R1
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Figure 13 Noninverting amplifier.
Figure 14 Diferential amplifier.
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Figure 15 Gain magnitude versus frequency.
Figure 16 Define half–power frequency and half–power bandwidth.
Differential Amplifier (in Figure 14)
Given R1 = R3 and R2 = R4 :
R2
(Vin1 − Vin2 )
R1
R2
AV = −
R1
Vout = −
Gain as a Function of Frequency in Fig. 15
Half-Power Frequency and Bandwidth in Fig. 16
The half–power
frequencies: the frequencies for which the voltage (or current) gain
√
magnitude is 1/ 2 times the midband gain magnitude. (the output power decreases by 1/2
of input power)
B: Half–power bandwidth.
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Figure 17 For Problem 4
2
Problems
1. A certain noninverting amplifier has a voltage–gain magnitude of 50. The input
voltage is vi (t) = 0.1 sin(2000πt).
(a) Find the expression for the output voltage vo (t).
(b) Repeat for an inverting amplifier.
2. An amplifier has an input resistance of 2000 Ω, an output resistance of 25 Ω, and an
open–circuit voltage gain of 500. The source has an internal voltage of Vs = 20 mV
rms and a resistance of Rs = 500 Ω. The load resistance is RL = 75 Ω. Find the
voltage gains Av = Vo /Vi and Avs = Vo /Vs . Find the current gain and the power
gain.
3. Assume that we can change the load resistance in Exercise 3. What value of load
resistance maximizes the power gain? What is the power gain for this load resistance?
4. Acircuit known as a summer is shown in Fig. 17.
(a) Use the ideal op-am assumption to solve for the output voltage in terms of the
input voltages and resistor values.
(b) What is the input resistance seen by vA ?
(c) By vB ?
(d) What is the output resistance seen by RL ?
2304154 Physics and Electronics (file: lec08 2.tex)
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