Lecture 8 Amplifiers (Basics)

Transcription

1 Lecture 8 Amplifiers (Basics)

2 EE 101 Schedule Version (supersedes version of date mistake) Class Lecture Date Topic Reading Ahead Homework Quiz Introduction Review Math Fundamentals of Electrical Engineering A & S Ch 1 Pre-Req Circuit Laws, Voltage & Current Dividers A & S Ch Node/Loop Analysis A& S Ch 3 Hmwk 1 Due Node/Loop Analysis Thévenin Equivalent Circuits A & S Ch Norton Equivalent Circuits Hmwk 2 Due Amplifiers A & S Ch Review for Midterm Midterm Op Amps Hmwk 3 Due Op-Amp Circuits Op-Amp Circuits Hmwk 4 Due Inductance and Capacitance A & S Ch First Order Transient Response A & S Ch RC/RL Circuits, Time Dependent Op Amp Circuits Hmwk 5 Due Second Order Transient Response Review for Midterm 2 Hmwk 6 Due Midterm Sinusoidal Signals, Complex Numbers, Phasors Phasor Circuits Hmwk 7 Due Veteran s Day AC Power, Thevenin Fourier Analysis, Low Pass Filters, Decibels Bode Plot, High Pass Filter, Series Resonance Hmwk 8 Due High Pass Filters, 2nd Order Filters, Active Filters, Resonances Magnetic Circuits, Materials Hmwk 9 Due Thanksgiving Day Mutual Inductance & Transformers TBD Hmwk 10 Due Review for Final at normal class time and place Final Exam Thursday, December 8th (noon to 3 pm)

3 Overall Goals 1. Use various amplifier models to calculate amplifier performance for given sources and loads. 2. Compute amplifier efficiency. 3. Understand the importance of input and output impedances of amplifiers.

4 Outline (Lecture 8) Basic amplifier concepts Cascaded amplifiers Power supplies and efficiency

5 Essence of an Amplifier

6 BASIC AMPLIFIER CONCEPTS Ideally, an amplifier produces an output signal with identical waveshape as the input signal, but with a larger amplitude.

7 Inverting and Non-inverting Amps

8 Inverting versus Non-inverting Amplifiers Inverting amplifiers have negative voltage gain, and the output waveform is an inverted version of the input waveform. Non-inverting amplifiers have positive voltage gain.

9 Voltage-Amplifier Model Input Output The input resistance R i is the equivalent resistance we see when looking into the input terminals of the amplifier. R o is the output resistance. It causes the output voltage to decrease as the load resistance becomes smaller. A voc is the open circuit voltage gain.

10 Current Gain

11 Power Gain Upper case V and I indicate Root Mean Square (RMS) values, i.e. the effective values of a fluctuating current or voltage.

12 Root Mean Square (RMS) Values V (t) = V m cos(ωt +ϑ) The average value of cos (ωt+ϕ) is zero. This is the squared version of the signal, and its mean value is ½. P Average = 1 T T 0 pdt = 1 T T 0 V m 2 cos 2 (ωt +ϑ) R dt = 1 R 1 T T V m 0 2 cos 2 (ωt +ϑ) = V 2 rms R For house power the 110 to 120 volts we are familiar with is the RMS value and the peak value is (110/0.707) or ~ 156 volts. Meters typically read RMS on the AC voltage scale unless noted otherwise.

13 Example I i Find the voltage gain, the current gain and the power gain:

14 Impedance Match for Max Power into Load 500Ω 25Ω 20 mv rms 2000Ω 500V i 25Ω What load resistance maximizes the power gain? From the Thevenin equivalent model we know that the maximum power delivered to a load is when the load resistance is equal to the Thevenin resistance of 25Ω. A v = V o R = A L 25 V voc = (500) i R o + R L = 250 G = (A v ) 2 R i R L = (250) = 5x106

15 CASCADED AMPLIFIERS

16 Example 11.2 Find the voltage gain for each stage and for the overall cascade connection:

17 Simplified Models for Cascaded Amplifier Stages First, determine the voltage gain of the first stage accounting for loading by the second stage. The overall voltage gain is the product of the gains of the separate stages. The input impedance is that of the first stage, and the output impedance is that of the last stage.

18 Input resistance and output resistance of the cascade:

19 Simplified Model A voc =1.5x10 4 R i =1MΩ R o =100Ω But how do we find this?

20 Finding the combined open circuit voltage gain A voc2 A v1 = A voc1 R i = 200 R i2 + R o =150 (same as before) A v2 = v o2 v i2 = 100v i2 v i2 = A voc 2 A voc = A v1 A v2 = (150)(100) =1.5x10 4 =100 ( for open output circuit) ( for combination)

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22 Heat P o >P i The additional power comes from the power supply. The efficiency is given by:

23 Find the input power, output power, supply power and the power dissipated in the amplifier. Also find the efficiency of the amplifier.

24 Input power: Output power: Supply power