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1510 Four sets of measurements were taken on the
same response variable of a process using four different sensors The true value of the response was known to be constant The four sets of data are shown in Figure P1510 Rank these data sets (and hence the sensors) with respect to: a Precision b Accuracy Measured value
Time (a) Measured value
Time (b) Part II
Electronics
Measured value True value
1518 Given the instrumentation ampli er of
Figure P1511, with the component values of Problem 1517, calculate the mismatch in gains for the differential components Express your result in dB Time (c) 1519 Given RF = 10 k and R1 = 2 k for the IA of
Figure 1516, nd R and R2 so that a differential gain of 900 can be achieved
Measured value True value
Section 3: Filters 1520 Replace the cutoff frequency speci cation of
Example 153 with C = 10 rad/s and determine the order of the lter required to achieve 40 dB attenuation at S = 24 rad/s lowpass lter with gain a Derive the relationship between output amplitude and input amplitude b Derive the relationship between output phase angle and input phase angle Time (d) 1521 The circuit of Figure P1521 represents a
Figure P1510
Section 2: Instrumentation Ampli ers 1511 For the instrumentation ampli er of
Figure P1511, nd the gain of the input stage if R1 = 1 k and R2 = 5 k
vb + R R2 R1 va + R 2 R R F vout + RF
CF Rr Rin Vout +
Figure P1521
1522 Consider again the circuit of Figure P1521 Let
Rin = 20 k , RF = 100 k , and CF = 100 pF Determine an expression for vout (t) if vin (t) = 2 sin (2,000 t) V lter of Figure 1522 Figure P1511
1512 Consider again the instrumentation ampli er of
Figure P154 Let R1 = 1 k What value of R2 should be used to make the gain of the input stage equal 50 1523 Derive the frequency response of the lowpass 1524 Derive the frequency response of the highpass lter of Figure 1522
1513 Again consider the instrumentation ampli er of
Figure P1511 Let R2 = 10 k What value of R1 will yield an inputstage gain of 16 input stage if R1 = 1 k and R2 = 10 k 1525 Derive the frequency response of the bandpass
lter of Figure 1522
1526 Consider again the circuit of Figure P1521 Let
1514 For the IA of Figure 1516, nd the gain of the 1515 For the IA of Figure 1516, nd the gain of the input stage if R1 = 15 k and R2 = 80 k
CF = 100 pF Determine appropriate values for Rin and RF if it is desired to construct a lter having a cutoff frequency of 20 kHz and a gain magnitude of 5 lter with a 10kHz cutoff frequency, a DC gain of 10, Q = 5, and VS = 15 V 1527 Design a secondorder Butterworth highpass 1528 Design a secondorder Butterworth highpass
lter with a 25kHz cutoff frequency, a DC gain of 15, Q = 10, and VS = 15 V
1516 Find the differential gain for the IA of
Figure 1516 if R2 = 5 k , R1 = R = R = 1 k , and RF = 10 k
1517 Suppose, for the circuit of Figure P1511, that
RF = 200 k , R = 1 k , and R = 2% of R Calculate the commonmode rejection ratio (CMRR) of the instrumentation ampli er Express your result in dB 1529 The circuit shown in Figure P1529 is claimed to
exhibit a secondorder Butterworth lowpass voltage gain characteristic Derive the characteristic and verify the claim 15
Electronic Instrumentation and Measurements
2 C 1 C/ 2 Vout + R2 = 1/a + 1 Vin R1 = 1/K + V1 1
R3 = 1/b
Figure P1529
1F V2 1
+ V3
1530 Design a secondorder Butterworth lowpass
lter with a 15kHz cutoff frequency, a DC gain of 15, Q = 5, and VS = 15 V
Figure P1534
1531 Design a bandpass lter with a low cutoff
frequency of 200 Hz, a high cutoff frequency of 1 kHz, and a passband gain of 4 Calculate the value of Q for the lter Also, draw the approximate frequency response of this lter 1535 The lter shown in Figure P1535 is called an
in nitegain multiplefeedback lter Derive the following expression for the lter s frequency response: H (j ) = (j )2 + (1/R3 R2 C1 C2 )R3 /R1 1 R1 C1
1532 Using the circuit of Figure P1529, design a
secondorder lowpass Butterworth lter with a cutoff frequency of 10 Hz
1533 A lowpass SallenKey lter is shown in
Figure P1533 Find the voltage gain Vout /Vin as a function of frequency and generate its Bode magnitude plot Show and observe that the cutoff frequency is 1/2 RC and that the lowfrequency gain is R4 /R3 1 R2 C1
1 R3 C1
j +
1 R3 R2 C 1 C2
R3 C2 C R1 R Vi R + _ R3 C1 Vo R2 +
C R4
Figure P1535
Figure P1533
1536 The lter shown in Figure P1536 is a Sallen and 1534 The circuit shown in Figure P1534 exhibits
lowpass, highpass, and bandpass voltage gain characteristics, depending on whether the output is taken at node 1, node 2, or node 3 Find the transfer functions relating each of these outputs to Vin , and determine which is which Key bandpass lter circuit, where K is the DC gain of the lter Derive the following expression for the lter s frequency response: H (j ) = (j )2 + j

