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 ECE 20B: Introduction to Electrical and Computer Engineering Winter 2003 resistance. - Infinite input resistance: Does not load input signal Recitation 1: Operational Amplifiers - Zero Output resistance: Does not “eat up” output signal Gain of ideal amplifier A = Voutput/Vinput 1 Ideal Amplifier…contd. Operational Amplifiers Op-amp: Schematic of amplifier RS + - vS 4 inputs, 1 output +V positive power supply Rout + vin 2 Rin + - + Avin Inverting input vL RL - Non-inverting input - (Figure 12.3) Vout Vout = AV(OL) (v+ - v-) Amplification factor, or gain, AV(OL) is called the open-loop voltage gain; typically O(105 – 107) Open-loop assumption (Rizzoni Eq. 12.10): = vin [A(RL / (Rout + RL)) (Rin / (RS + Rin))] vS + -V negative power supply Rin = equivalent resistance seen at input of amplifier; Rout = internal (output) resistance of amplifier vin = (Rin / (RS + Rin)) vS vL = Avin (RL / (Rout + RL)) Output goes positive when non-inverting input (+) goes more positive than the inverting input (-), and vice-versa. _ 3 Operational Amplifier…contd. iin = 0 (“Golden Rule #2: The inputs of an op-amp draw no current.” – cf. Horowitz and Hill textbook) 4 Square wave output Consider some typical values: z z z Ri = 105 – 1012 Ohms Ro = 1 – 50 Ohms A = 105 – 107 V/V Suppose A = 105 , +V = 12V, -V = -12V z z z z 120uV achieves saturation (output voltage cannot exceed supply) Current into input terminals is 120uV / 105 Ohms = 120 x 10–11 A (open circuit) Rout is low, approximated as 0 Æ Vout = A(v+ - v-) For a sinusoid, the output of Op-amp is a square wave with only two distinct voltage levels –1V and +1V How does op-amp output vary with A when v- is sinusoidal? • A continuous sinusoid generates a square wave as output We can represent the voltage levels as ‘0’ (= -1V) and ‘1’ (= +1v). 5 Op-amp is a primitive digital element 6 Op - amp comparator Op - amp – Digital output in open loop mode In comparator configuration of Op-amp, the inverting input is connected to ground and input is given in noninverting 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. Output of comparator in open-loop mode 7 Feedback Source: http://www.tonmeister.ca/main/textbook/electronics/12.html Inverting (gain = negative) Amplifier Negative feedback: R2 process of coupling the output back in such a way as to cancel some of the input z z z 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 A “self-balancing mechanism” that allows amplifier to preserve zero potential difference between its input terminals Feedback can also be positive (oscillators, etc.) R1 A in B Point B is at ground Æ Point A is also (G.R. #2) Æ voltage across R2 is Vout , and voltage across R1 is Vin G.R. #1 Æ across R2 is Vout / R2 = - Vin / R1 Voltage gain = across R2 is Vout / Vin = - R2 / R1 Observe: voltage gain is so high that a tiny voltage between input terminals will swing the output over its entire range z 8 Ignore this small voltage Æ “Golden Rule #1: The output attempts to do whatever is necessary to make the voltage between the inputs zero.” 9 10 Non - Inverting (gain = positive) Amplifier Voltage follower VA comes from a voltage divider Æ VA = VoutR1 / (R1 + R2) G.R. #2 Æ VA = Vin Gain = Vout / Vin = 1 + R2 / R1 Output voltage follows input voltage. Gain = 1 since feedback resistance R2 = 0 Is used as a buffer to isolate input signal from output 11 12 Mixer amplifier Op - amp oscillators An Op-amp with a A mixer amplifier mixes several input signals and positive feedback produces an oscillator amplifies them at various levels Inputs from several sources are connected to the An oscillator produces inverting input of the Op-amp as shown output voltage without any input signal The gain can be varied by modifying the series resistances 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 The total voltage at the output will be Vout = -(v1 (Rf/R1) + v2 (Rf/R2)) 13 Op - amp oscillators…contd a single R and C produces a square wave output with a frequency of 1/(2πRC) 14 Op - amp summary 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 C1 C2 +V C3 R1 R2 R3 vout + -V 15 Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/Op-ampcon.html 16