Department of Electrical Engineering, IIT Kanpur                                                                                                                                                                      ESC 201A: Introduction to Electronics  

 

                      4th Sept. 2014

            Home Assignment-5

1. Sketch the Bode magnitude plots of the following transfer functions. Indicate the coordinates of all corners and all slopes on the plot.

(a) H(jω) = ( )( )( )

2

2

10 j100ω10+jω 100+jω

(b) H(jω) = ( )( )( )

310 jω+110+jω 20+jω

2. The Bode magnitude plots of two transfer functions H1(jω) and H2(jω) are shown in the Fig. 1(a) and Fig. 1(b). Determine the functions H1(jω) and H2(jω).

Fig. 1(a): Bode Plot for H1(jω)

Fig. 1(b): Bode Plot for H2(jω)

Department of Electrical Engineering, IIT Kanpur                                                                                                                                                                      ESC 201A: Introduction to Electronics  

3. Determine the transfer function H(jω)= ( )( )

c

s

V jωV jω

of the circuit shown in Fig 2. Determine the

frequency (ω0, in rad/s) at which the phase of H(jω0) is -900. What is the magnitude of H(jω0) in dB?

10 Ω

125 Ω4 H

0.105 V1

1.5V 0.25 µF

+Vc-

+ V1 -

Fig. 2

4. Determine the resonant frequency of the circuit shown in Fig 3.

+Vo-

1 µF

2Vo

5 mH

0.25 Ω

Fig. 3

5. A series resonant network consists of a 50 Ω resistor, a 4 mH inductor and 0.1 µF capacitor. Calculate the values for (a) ω0 (b) f0 (c) Q0 (d) B

(e) ω1 (f) ω2 (g) Zin at 45 krad.s-1

(h) The ratio of magnitudes of the capacitor impedance to the resistor impedance at 45 krad.s-1

Department of Electrical Engineering, IIT Kanpur                                                                                                                                                                      ESC 201A: Introduction to Electronics  

6. A transfer function is given by

H(jω) = ( )( )( )2

- 10+j10ω 10+jωjω

.

a) Draw the asymptotic Bode plots of the magnitude and phase of the transfer function, for the angular frequency ω ranging between 0.1 rad/sec . and 100 rad/sec .clearly highlight all the silent features of the plots.

b) Using the Bode analysis technique, analytically determine the asymptotic values of the magnitude and phase of the transfer function at ω = 5 rad/sec. Compare these values with those predicted by the plots done in part (a).

7. Design a parallel resonant circuit for an AM radio so that a variable inductor can adjust the resonant frequency over the AM broadcast, 535 kHz to 1605 kHz, withQ0 = 45 at one end of the band and Q0 ≤ 45 throughout the band. Let R= 20kohm. Specify values for C, Lmin, Lmax.

8. For the circuit shown in Fig.4, calculate the resonant frequency, ω0 ..Also compute the quality factor and maximum value of |Vc(jω)|. Plot |Vc| verses ω.

10 Ω

125 Ω 4 H

0.105 V1Vs

0.25 µF+Vc-

+ V1 -

Fig. 4

Department of Electrical Engineering, IIT Kanpur                                                                                                                                                                      ESC 201A: Introduction to Electronics  

9. (a) Find the Q of the circuits shown in Fig. 5(a) and Fig. 5(b) Use basic definition of Q.

(b) Find the values for Rp and Xp(in terms of Rs, Xs and Q) so that the parallel network shown in Fig.5(b) is equivalent to series network shown in Fig. 5(a) at some single specific frequency.

jXs

RsI

+

V

-

jXpRp

I

+

V

-

Fig 5(a) Fig 5(b)

10. Determine ‘Q’ for dropping the following onto a smooth concrete floor from an arbitrary chosen height.

a) Ping Pong Ball b) Quarter c) A textbook

You may assume measurement conditions as per your choice, Also give your observations in detail (For eg. Averaging or statistical Analysis). Note: This example can be used to illustrate parallel resonance and is for general discussion only.

11. Draw a bode magnitude plot for the transfer function given below :

H(jω) = ( )( )( ) ( )

2

2

jω+1 jω+1000

jω+10 jω+10000⎡ ⎤⎣ ⎦