Tutorial 12003

LEVEL 3 : 3015 COMMUNICATIONS, SIGNALS AND SYSTEMS 2003

Tutorial number 1

In all of the questions below, there is one box for the numerical answer and one box for the units. 1. The output voltage of an ideal sinusoidal steady state voltage source operating at a

frequency of 50 Hz is represented by a phasor of 8j V r.m.s. Determine the maximum instantaneous voltage, the minimum instantaneous voltage and the value at time t = 0 of the instantaneous voltage.

Maximum Minimum

Value at t = 0 2. The simple RC circuit below, which has r = 100 and C = 15.92 F, is excited by a

sinusoidal voltage source VS of magitude 240V r.m.s. at 50 Hz. Determine

Cr

VS VC

++

_ _

(a) The peak voltage across the capacitor

(b) The phase, in degrees, of the voltage across the capacitor relative to the phase of the source voltage VS. 3. The network shown below has a sinusoidal internal source voltage of 20 Vpp and an

internal impedance of 50 + j 30 ohms. Determine the load impedance which can draw the maximum power from this source, and the available source power, i.e. the power delivered to that load impedance.

3015 Communications, Signals and Systems 2003 Tutorial No 1. Page 2

+

_V = 20VS pp

50 + 30 ohm j

Load impedance

Available source power

4. For the one-port network shown below, determine the parameters of the Norton

equivalent circuit also shown.

100 ohm

200

ohm

A

A

B

B

0.5V

I

The diode has at a forward voltage of 0.5 V a forward current of 10 mA.

R

+

_

Current I

Resistance R 5. An ammeter with a burden of 10 ohms is used to determine the short circuit current of

the d.c. network below. With the positive terminal of the ammeter connected to terminal A of the network and the negative terminal connected to terminal B of the network, the ammeter reads -300 mA. Determine the value of the current source I.


20 ohmI

A

B

Current 6. A square wave of voltage oscillates as shown in the figure below between the values

of -1 V and 2 V at a rate of 100 Hz. Determine the r.m.s. value of the voltage waveform.

v(t)

t

+2V

-1V

r.m.s value 7. For the network shown below, operating in a system with characteristic impedance of

50 at both ports, determine the insertion loss in dB.

.

50 ohm

V V21 Port 1 Port 2

3015 Communications, Signals and Systems 2003 Tutorial No 1. Page 4 8. An inductor is wound as shown in the figure below on a toroidal ferrite core of

relative permeability 13, mean diameter of 26 mm, and round cross section of diameter 6 mm. The inductor has a total of 500 turns, many more than are shown. Determine:

i6mm

26m

m

(a) the magnitude of magnetic field H in the core at the mean diameter when a

current of 100 mA flows in the winding;

Magnetic field (b) the magnetic flux density B in the core at the same position and under the

same conditions; and

Magnetic flux density (c) The self inductance, under the assumption that the magnetic field is uniform

across the cross section and has the value calculated above for the mean diameter.

Self inductance 9. For the network shown below, determine the parameters of the impedance matrix.

100 ohm

100 ohmi 1

v v

i 2

21

Z11 Z12

Z21 Z22

3015 Communications, Signals and Systems 2003 Tutorial No 1. Page 5 10. In the resonant circuit shown below, L = 16H, r = 23 , C = 455 pF and the peak

value phasor VS, which is real and is of magnitude 1 V, excites the circuit at its resonant frequency.

CL r

VS VC

++

_ _

Calculate:

(a) the resonant frequency

(b) the quality factor

(c) the dynamic impedance at resonance

(d) the magnitude of VC

(c) the phase, in degrees, of VC 11. Calculate the resistance of a 1000 metre length of round copper wire of diameter 2

mm and conductivity 5.8 x 107 S/m.

Resistance 12. Determine the inductance of the single inductor which is equivalent to the

combination of a 6 H inductor and a 12 H inductor in parallel.

Inductance

3015 Communications, Signals and Systems 2003 Tutorial No 1. Page 6 13. For the network at the left in the figure below, calculate the parameters of both the

Thevenin and Norton equivalent circuits, shown as prototypes on the right in the figure below, when such circuits exist. If one or more of those circuits does not exist, write the work none in the box for the relevant parameter, and leave the associated units box blank.

5

5V+

_

A

B

B

A

I

5V

+

_

A

B

Thevenin voltage Thevenin resistance

Norton current Norton resistance

14. For the network at the left in the figure below, calculate the parameters of both the

Thevenin and Norton equivalent circuits, shown as prototypes on the right in the figure below, when such circuits exist. If one or more of those circuits does not exist, write the work none in the box for the relevant parameter, and leave the associated units box blank

5A

10V+

_

A

B

B

A

I

2V

+

_

A

B


Norton current Norton resistance


15. A layer of aluminium 300 nm thick and conductivity 3 x 107 S/m in used to fabricate

thin strips of interconnecting wire between the elements of a microcircuit. Assuming a uniform current distribution over the cross section of this material, determine the surface resistivity in ohms per square of the interconnecting wires.

Surface resistivity 16. The RC series network shown below is fed from a square wave voltage source of

frequency 1 kHz and internal impedance of 50 ohms. Determine the 10% to 90% rise time of the output voltage.

17. A DC bridge circuit, in which the output terminals are labelled as A and B, appears in the Figure below.

A B

3 k

6 k

6 k

6 V+-

3 k

E

(a) For the part of the circuit consisting of the 6V source, the leftmost two resistors, and the terminals A and E, detemine the parameters of the Thevenin equivalent circuit shown below.


A

V

R

E

+

_

TH

TH

Thevenin voltage Thevenin resistance (b) For the part of the circuit consisting of the 6V source, the rightmost two

resistors, and the terminals B and E, detemine the parameters of the Thevenin equivalent circuit shown below.

E

V

RB

+

_

TH

TH


(c) Making use of the two results above, determine the parameters of the Thevenin equivalent circuit, shown below, for the original bridge circuit.

A

V

R

B

+

_

TH

TH


Tutorial 12003

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