Signals and Systems - Electrical Engineering

Problems 159

FIGURE 2.21

Problem 2.5: p-n diode and i-v characteristic.

−

+

0

i(t)

i(t)

Is

v(t)

v(t)

(a) Consider the voltagev(t)as the input and the currenti(t)as the output of the diode. Is the p-n diode a

linear system? Explain.

(b)Anideal diodeis such that when the voltage is negative,v(t) < 0 , the current is zero (i.e., open circuit),

and when the current is positive,i(t) > 0 , the voltage is zero or short circuit. Under what conditions

does the p-n diode voltage–current characterization approximate the characterization of the ideal

diode? Use MATLAB to plot the current–voltage plot for a diode withIs=0.0001andkT/ 1 =0.026,

and compare it to the ideal diode current–voltage plot. Determine if the ideal diode is linear.

(c)Consider the circuit using an ideal diode in Figure 2.22, where the source is a sinusoid signalv(t)=

sin( 2 πt)u(t)and the output is the voltage in the resistorR= 1 orvR(t). PlotvR(t). Is this system

linear? Where would you use this circuit?

FIGURE 2.22

Problem 2.5: ideal diode circuit.

−

+

R

Ideal diode

v(t)

i(t)

2.6. Capacitor/inductor circuit
Consider the circuit in Figure 2.23, where the value of the capacitor isC=1 F, and the initial condition
isvc( 0 )=−1 volts. Assume the input is the current sourceis(t)and the voltage in the capacitorvc(t)the
output.
(a) Let the current in the circuit beis(t)=u(t)−u(t− 1 ), and the initial voltage in the capacitor bevc( 0 )=
−1 volts. Plot the voltage in the capacitorvc(t)for all times. Suppose then we double the current,
is(t)= 2 (u(t)−u(t− 1 )), but keep the same initial condition. Plot the voltage in the capacitorvc(t)for
all times, and compare it with the one obtained before. Is the capacitor with non-zero initial conditions
a linear system? Explain.
(b)Consider the dual circuit where the value of the inductor isL=1 H, the initial current in the inductor
isiL( 0 )=−1 amps, and the input is the sourcevs(t). Letvs(t)=u(t)−u(t− 1 ). Plot the corresponding
currentiL(t)for all times. Double the voltage sourcevs(t)=2[u(t)−u(t− 1 )], and plot the correspond-
ing current in the inductoriL(t)for all times. Compare the two currents and determine if the inductor
with the initial current is linear. What ifiL( 0 )= 0?