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Figure P1257
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Operational Ampli ers
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1258 Consider a differential ampli er We would
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desire the common-mode output to be less than 1 percent of the differential-mode output Find the minimum dB common-mode rejection ratio (CMRR) to ful ll this requirement if the differential mode gain Adm = 1,000 Let v1 = sin (2,000 t) + 01 sin (120 t) V v2 = sin (2,000 t + 180 ) + 01 sin (120 t) V v1 + v2 vo = Adm (v1 v2 ) + Acm 2
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Figure P1261
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1262 Given the unity-gain bandwidth for an ideal 1259 Square wave testing can be used with operational
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ampli ers to estimate the slew rate, which is de ned as the maximum rate at which the output can change (in V/ s) Input and output waveforms for a noninverting op-amp circuit are shown in Figure P1259 As indicated, the rise time, tR , of the output waveform is de ned as the time it takes for that waveform to increase from 10 percent to 90 percent of its nal value; ie, tR = tB tA = (ln 01 ln 09) = 22 where is the circuit time constant Estimate the slew rate for the op-amp op-amp equal to 50 MHz, nd the voltage gain at a frequency of f = 500 kHz
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1263 The open-loop gain A of real (nonideal) op-amps
is very large at low frequencies but decreases markedly as frequency increases As a result, the closed-loop gain of op-amp circuits can be strongly dependent on frequency Determine the relationship between a nite and frequency-dependent open-loop gain AV (OL) ( ) and the closed-loop gain AV (CL) ( ) of an inverting ampli er as a function of frequency Plot AV (CL) versus Notice that RF /RS is the low-frequency closed-loop gain
1264 A sinusoidal sound (pressure) wave p(t)
impinges upon a condenser microphone of sensitivity S (mV/kPa) The voltage output of the microphone vs is ampli ed by two cascaded inverting ampli ers to produce an ampli ed signal v0 Determine the peak amplitude of the sound wave (in dB) if v0 = 5 VRMS Estimate the maximum peak magnitude of the sound wave in order that v0 not contain any saturation effects of the op-amps
t, s 10 10 0 % 90 % Vout 20 30 40 Vm = 15 V
1265 If, in the circuit shown in Figure P1265:
t, s
10 % 101 145 t v tB 301 345
vS1 = 28 + 001 cos( t) V vS2 = 35 0007 cos( t) V Av1 = 13 Av2 = 10 = 4 krad/s determine the: a Common- and differential-mode input signals b Common- and differential-mode gains c Common- and differential-mode components of the output voltage d Total output voltage e Common-mode rejection ratio
+ R2
+ v S1
Figure P1259
1260 Consider an inverting ampli er with open-loop
gain 105 With reference to equation 1218, a If RS = 10 k and RF = 1 M , nd the voltage gain AV (CL) b Repeat part a if RS = 10 k and RF = 10 M c Repeat part a if RS = 10 k and RF = 100 M d Using the resistor values of part c, nd AV (CL) if AV (OL)
_ RF
+ vo _
a If the op-amp of Figure P1261 has an open-loop gain of 45 105 , nd the closed-loop gain for RF = RS = 75 k , with reference to equation 1218 b Repeat part a if RF = 5(RS ) = 37,500
+ v S2
Figure P1265
Part II
Electronics
1266 If, in the circuit shown in Figure P1265:
vS1 = 35 + 001 cos( t) V vS2 = 35 001 cos( t) V Avc = 10 dB Avd = 20 dB 3 = 4 10 rad/s determine the: a Common- and differential-mode input voltages b The voltage gains for vS1 and vS2 c Common-mode component and differential-mode component of the output voltage d The common-mode rejection ratio (CMRR) in dB
d The common-mode component and the differential-mode component of the output voltage e The common-mode rejection ratio (CMRR) in dB
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