1. 1 ECE 20B: Introduction to Electrical and Computer Engineering Winter 2003 Recitation 1: Operational Amplifiers

2. 2 Ideal Amplifier  “Amplifies” weak (= low voltage) electrical signals. E.g. Cassette/CD player, strain gauge, accelerometer.  Ideal amplifier: Output Signal = Gain x Input Signal  Ideal amplifier: has infinite input resistance, zero output resistance. - Infinite input resistance: Does not load input signal - Zero Output resistance: Does not “eat up” output signal  Gain of ideal amplifier A = V output /V input

3. 3 Ideal Amplifier…contd.  Schematic of amplifier + vSvS R in Av in - + - R out + + - v in RLRL - vLvL RSRS  (Figure 12.3) R in = equivalent resistance seen at input of amplifier; R out = internal (output) resistance of amplifier  v in = (R in / (R S + R in )) v S  v L = Av in (R L / (R out + R L )) = v in [A(R L / (R out + R L )) (R in / (R S + R in ))] v S

4. 4 Operational Amplifiers  Op-amp: 4 inputs, 1 output Inverting input + _ +V positive power supply Vout -V negative power supply Non-inverting input Output goes positive when non-inverting input (+) goes more positive than the inverting input (-), and vice-versa.  V out = A V(OL) (v + - v - )  Amplification factor, or gain, A V(OL) is called the open-loop voltage gain; typically O(10 5 – 10 7 )  Open-loop assumption (Rizzoni Eq. 12.10): i in = 0 (“Golden Rule #2: The inputs of an op-amp draw no current.” – cf. Horowitz and Hill textbook)

5. 5 Operational Amplifier…contd.  Consider some typical values: l R i = 10 5 – 10 12 Ohms l R o = 1 – 50 Ohms l A = 10 5 – 10 7 V/V  Suppose A = 10 5, +V = 12V, -V = -12V l 120uV achieves saturation (output voltage cannot exceed supply) l Current into input terminals is 120uV / 10 5 Ohms = 120 x 10 –11 A (open circuit) l R out is low, approximated as 0 l  V out = A(v + - v - )  How does op-amp output vary with A when v - is sinusoidal? A continuous sinusoid generates a square wave as output

6. 6 Square wave output  For a sinusoid, the output of Op-amp is a square wave with only two distinct voltage levels –1V and +1V  We can represent the voltage levels as ‘0’ (= -1V) and ‘1’ (= +1v).  Op-amp is a primitive digital element

7. 7 Op-amp comparator  In comparator configuration of Op-amp, the inverting input is connected to ground and input is given in non- inverting input.  If the input signal is slightly positive, then the output jumps to V + ( = supply voltage)  If the input signal is slightly negative, then the output jumps to V - (= - supply voltage)  The output jumps between two extremes V+ and V- since the open-loop gain is very high.

8. 8 Op-amp – Digital output in open loop mode Source: http://www.tonmeister.ca/main/textbook/electronics/12.html  Output of comparator in open-loop mode

9. 9 Feedback  Negative feedback: process of coupling the output back in such a way as to cancel some of the input l Lowers gain, but amplifier characteristics become less dependent on characteristics of the open-loop (no-feedback) amplifier; eventually depend only on properties of the feedback network itself l A “self-balancing mechanism” that allows amplifier to preserve zero potential difference between its input terminals l Feedback can also be positive (oscillators, etc.)  Observe: voltage gain is so high that a tiny voltage between input terminals will swing the output over its entire range l Ignore this small voltage  “Golden Rule #1: The output attempts to do whatever is necessary to make the voltage between the inputs zero.”

10. 10 Inverting (gain = negative) Amplifier  Point B is at ground  Point A is also (G.R. #2)   voltage across R 2 is V out, and voltage across R 1 is V in  G.R. #1  across R 2 is V out / R 2 = - V in / R 1  Voltage gain = across R 2 is V out / V in = - R 2 / R 1 in A B R1R1 R2R2

11. 11 Non-Inverting (gain = positive) Amplifier  V A comes from a voltage divider  V A = V out R 1 / (R 1 + R 2 )  G.R. #2  V A = V in  Gain = V out / V in = 1 + R 2 / R 1

12. 12 Voltage follower  Output voltage follows input voltage.  Gain = 1 since feedback resistance R 2 = 0  Is used as a buffer to isolate input signal from output

13. 13 Mixer amplifier  A mixer amplifier mixes several input signals and amplifies them at various levels  Inputs from several sources are connected to the inverting input of the Op-amp as shown  The gain can be varied by modifying the series resistances  The total voltage at the output will be V out = -(v 1 (R f /R 1 ) + v 2 (R f /R 2 ))

14. 14 Op-amp oscillators  An Op-amp with a positive feedback produces an oscillator  An oscillator produces output voltage without any input signal  Positive feedback refers to the case where output is fed back to the input such that it augments the input signal  The Op-amp circuit with a single R and C produces a square wave output with a frequency of 1/(2  RC)

15. 15 Op-amp oscillators…contd  RC phase-shift oscillators are used to produce sinusoidal outputs  A RC network is used in the positive feedback loop to shift phase by desired amount  A simple sinusoidal oscillator shown below consists of three CR ladders cascaded and given to inverting input of Op-amp R1R1 C1C1 - + v out R2R2 R3R3 C2C2 C3C3 +V -V

16. 16 Op-amp summary Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/Op-ampcon.html