Electronics signal processing control and communications
Question 1 (4 marks)
a. A sinusoidal current, 5 mA in amplitude, flows in a resistor of 250 W. Calculate the mean-squared
voltage across the resistor. Give your answer to 3 significant figures.(2 marks)
b. Wide band noise with a power density of 3 × 10 W Hz is present at the input of a receiver with a
bandwidth of 20 kHz. Within the noise is a wanted signal with a power density of 30 × 10 W Hz and
a bandwidth of 5 kHz. What is the signal-to-noise ratio at the receiver’s input if the receiver’s bandwidth
is centred on the wanted signal? Give your answer as a natural ratio and in decibels.
(2 marks)
–11 –1
–11 –1
Question 2 (4 marks)
a. A signal that is described by the equation v (t) = 35 sin (10t) mV is applied to the input of a filter. The
output signal from the filter is v (t) = 7 sin (10t – 0.44 ) mV. Express the gain as a voltage ratio.
(3 marks)when in and when out
b. The frequency of the input to the filter in (a) changes but the amplitude is left unchanged. The output is
now found to be v (t) = 0.7 sin (100t – 0.499 ) mV. What is the new gain as a voltage ratio?
(1 mark) out
Question 3 (4 marks)
a. A first-order low-pass filter, such as the one shown in Figure 2.5 on p. 18 of Book 1, with a cut-off
frequency of 5 kHz, has a capacitor of 10 nF. What value of resistor is required?(3 marks)
b. For the filter in (a), what is the gain of the filter at 500 kHz? Express you answer in decibels. (Hint: this
requires hardly any calculation.)(1 mark)
Question 4 (4 marks)
a. A second-order RLC band-pass filter like that in Book 1, p. 28, Figure 2.12(c) uses a capacitor of 125 pF.
The filter is required to have a resonant frequency of 100 kHz. What value of inductance is required?
Give your answer to 3 significant figures.(3 marks)
b. For the filter in (a), what value of R will give a 4 kHz pass band? Give your answer to 2 significant
figures.(1 mark)