Electrical Engineering Questions and Answers

Transmission lines

1. (a) A cable is 15 km long and has the following distributed constants all per loop kilometre at a frequency of 100 kHz.

(i) the signal phase shift in degree 5 km down the line.

(ii) the electrical length of the line.

(iii) the relative permittivity of the dielectric material of the line.

(b) A lossless transmission line has a characteristic impedance of 50 Ω is terminated with a load. The load impendence is (85 + j 40) Ω. Calculate the magnitude of the reflection coefficient and the Voltage Standing Wave Ratio along the line.

(c) An electrical product you are developing has undergone an electric field radiated emission test in order to comply with the European Union Directive for electromagnetic compatibility for CE Marking. The test result exceeds the electric field radiated emission limit for 10 m test distance of 30 dBµV/m by 15 dB at a frequency of 55 MHz and is found to be due to radiation from a 2 m long signal cable. Calculate the common mode interference current on the signal cable that could cause the test failure.

(d) The analysis of an electromagnetic compatibility scenario requires an understanding of the source of electromagnetic energy, the coupling mechanism and the victim equipment. Briefly describe four possible coupling mechanisms.

2. (a) Find the bandwidth of a band-pass filter whose cut-off frequencies are 3.2 kHz and 3.9 kHz and determine whether it is a wide-band or a narrow-band filter. Explain your reasoning.

(b) A low-pass Butterworth filter having a maximum low-frequency gain of 1 and a cut-off frequency of 4 kHz is to be designed so that its gain is no less than 0.92 at 3 kHz. Find the minimum order of the filter.

(c) (i) Design a second-order, IGMF (infinite-gain, multiple-feedback) bandpass filter with a centre frequency of 20 kHz and a bandwidth of 4 kHz. The gain should be 2 at 20 kHz (Use the provided block diagram of Fig.2c and Table 2c).

Table 2c Second-Order Multiple-Feedback Bandpass Filter Designs (Q=5)

(c) (ii) The input to the above filter has the following components: V1 (6 V-rms at 2 kHz), V2 (2 V-rms at 20 kHz) and V3 (10 V-rms at 100 kHz). Calculate the rms values of these components in the filter’s output.

3.Instrumentation and Measurement

A thermistor has had the resistances measured at three reference temperatures determined using a traceable temperature measurement system. The values are: Temp.

For the following, ensure you show your working at each stage and include explanations at each stage.

(a) Determine the Steinhart-Hart coefficients for this thermistor by solving a system of three linear simultaneous equations using the following equation:

(b) Use linear regression assuming identically and independently normally distributed errors to approximate the relation between the temperature and resistance for this thermistor.

(c) Compare, with the use of a plot, the two functions derived in (a) and (b), for 10 temperatures spanning the range of the original measurements. Also include the original measurements and appropriate labels.

(d) Use the result from (a) to design a Wheatstone quarter bridge circuit that has zero volts differential output for fifty five degrees Celsius with an approximately linear range of output voltages for a load with infinite input impedance. Ensure the bridge output voltage has a reasonable range of values for the range of temperatures considered here (e.g. -1V to +2V). To help demonstrate your achieved result, plot the differential voltage output as a function of temperature over the specified range. Quantify the non-linearity of the resulting function. What might affect the value of this non-linearity? Why?