About Electronics and Communication
Electronics and communication questions in a recruitment paper are circuit arithmetic, the gain of an amplifier, a time constant, a decibel figure, a resonant frequency, a rectifier value, the band an amplitude modulated signal occupies and the rate at which it must be sampled. This topic covers all of those areas on one page, so that the subject can be practised as a whole rather than in fragments.
What you need to understand
- Ohm law holds the subject together: V = I R. Resistances in series add; resistances in parallel add as reciprocals, and the combination is always smaller than the smallest of them.
- Kirchhoff laws are the two bookkeeping rules: the currents into a node add to zero, and the voltages round a closed loop add to zero. Almost every circuit question is one of them written out.
- An ideal operational amplifier has an enormous gain and takes no current at its inputs. With negative feedback, that forces the two inputs to sit at the same voltage, and the gain is then fixed by the resistors alone.
- The inverting amplifier has a gain of minus the feedback resistor over the input resistor. The non-inverting amplifier has a gain of one plus that ratio, which is why its gain is always at least one.
- A capacitor charging through a resistor has a time constant of R C. It reaches about 63 per cent of the supply in one time constant and is called fully charged after about five.
- A resistance in kilohms multiplied by a capacitance in microfarads gives a time in milliseconds. That pairing is worth remembering; it removes a conversion from most questions.
- A decibel is ten times the logarithm to base ten of a power ratio, or twenty times the logarithm of a voltage or current ratio. A doubling of power is 3 dB and a tenfold increase is 10 dB, whatever the absolute level.
- An inductor and a capacitor resonate at one over two pi times the square root of their product. With the inductance fixed, the frequency varies as one over the square root of the capacitance.
- A diode conducts in one direction only. Half wave rectification gives one pulse per cycle, with an average of the peak over pi; full wave rectification gives two, with an average of twice the peak over pi.
- The root mean square value of a sine wave is its peak over the square root of two, about 0.707 of the peak. It is the value that matters for power and heating, and it is not the average.
- Amplitude modulation puts two sidebands on the carrier, one either side at the modulating frequency. The modulation index is the peak of the modulating signal over the carrier, and the bandwidth is twice the modulating frequency.
- A signal must be sampled at more than twice its highest frequency. Sample any slower and the high frequencies fold back into the band as aliases, which no filter can remove afterwards.
- A converter of n bits divides its range into two to the n levels, so its resolution is the range divided by that. Each extra bit halves the smallest change it can resolve.
- A NAND gate and a NOR gate are each enough on their own to build every other logic function, which is why they are the gates that get made.
How to work through these questions
- Write down what is asked for and in what unit before doing anything. Half the errors in this topic are unit errors rather than arithmetic ones.
- For an amplifier, identify which configuration it is first. The plus one in the non-inverting gain is the single commonest omission.
- For anything with a capacitor, work out whether the question is about the time constant itself, the voltage after a given time, or the time to reach a given voltage - they are three different sums.
- For a decibel question, decide whether the ratio given is of powers or of voltages. The factor of two between the two formulas turns on that alone.
- For a rectifier, note whether the wave is half wave or full wave and whether the average or the root mean square is wanted. The four numbers 0.318, 0.637, 0.707 and 1.414 cover all of them.
- For a sampling or bandwidth question, answer in the units asked for and check the size is sensible: a bandwidth in tens of kilohertz and a sampling rate in tens of thousands of samples are about right for audio.
Mistakes that cost marks
- Leaving the plus one out of the gain of a non-inverting amplifier, which gives a gain below one that the circuit cannot have.
- Using twenty times the logarithm on a ratio of powers, or ten times on a ratio of voltages. The answer is then exactly twice the right one.
- Multiplying a resistance in kilohms by a capacitance in microfarads and quoting the answer in seconds. The product is in milliseconds.
- Using the capacitance ratio itself to find a new resonant frequency instead of its square root.
- Quoting the root mean square value of a rectified sine wave when the average was asked for, or the average when the heating value was wanted.
- Treating the flow through an orifice plate as a straight proportion of the differential pressure. It goes as the square root, so the error grows with the differential.
- Adding a gauge pressure and an atmospheric pressure that were given in different units, or subtracting the atmosphere when the gauge was being read above it.
- Dividing a converter range by the number of bits rather than by two to the power of the bit count, which makes the resolution far too coarse.
Worked example
A non-inverting amplifier has a resistor of 2 k to ground and a feedback resistor of 10 k, and it is fed with 3 V. What is the output? A full wave rectified sine wave has a peak of 100 V: what is its average value, to the nearest volt?
- For the amplifier, the gain of a non-inverting stage is one plus the feedback ratio: 10 / 2 = 5, so the gain is 1 + 5 = 6.
- Check it against the circuit: a non-inverting amplifier cannot attenuate, and a gain of six is well above one, so the answer is of the right kind.
- The output is the gain times the input: 6 x 3 = 18 V.
- For the rectifier, a full wave rectified sine spends most of its time below its peak, and its average works out at two over pi of the peak.
- Two over pi is 0.6366, so the average is 0.6366 x 100 = 63.66 V, which is 64 V to the nearest volt. The root mean square value of the same wave would be 70.7 V, and the half wave average would be 31.8 V - both are offered as wrong answers, and both are quantities worth knowing.
Answer: 18 V from the amplifier; 64 V average from the rectifier
Practice questions with answers
A few Electronics and Communication questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A non-inverting amplifier has a resistor of 2 k between its inverting input and ground, and a feedback resistor of 8 k. With an input of 1 V, what is the output voltage, in volts?
Answer: Option D — with explanation
A non-inverting amplifier has a gain of one plus the ratio of the feedback resistor to the resistor to ground, because the feedback holds the inverting input at the same voltage as the non-inverting one and the two resistors then divide the output.
That ratio is 8 / 2 = 4, so the gain is 1 + 4 = 5.
The output is the gain times the input: 5 x 1 = 5 V. Leaving out the one gives a gain smaller than one, which no non-inverting amplifier can have - the output can never be weaker than the input.
Common mistakes
- 5/4 is not the answer: 5/4
- 10 is not the answer: 10
- 4 is not the answer: 4
Question 2
An amplifier takes an input of 1 mW and delivers an output of 10 mW. What is its power gain in decibels?
Answer: Option B — with explanation
A decibel is ten times the logarithm to base ten of a power ratio, so the working is 10 log10 of the output power divided by the input power.
The ratio is 10 / 1 = 10, and log10 of 10 is 1.0000, so the gain is 10 x 1.0000 = 10.0 dB.
Twenty times the logarithm is the form used for a ratio of voltages or currents, and using it on a ratio of powers gives twice the right answer. A doubling of power is 3 dB, and it is 3 dB however many times it is doubled - ten doublings are 30 dB, not 300.
Common mistakes
- 7 is not the answer: 7
- 20 is not the answer: 20
- 13 is not the answer: 13
Question 3
A circuit containing a 90 pF capacitor resonates at 120 kHz. With the same inductor and a 10 pF capacitor, what is the resonant frequency, in kHz?
Answer: Option C — with explanation
The resonant frequency of an inductor and a capacitor is one over two pi times the square root of their product, so it varies as one over the square root of the capacitance when the inductance is fixed.
The capacitance has gone from 90 pF to 10 pF, a factor of 1/9, so the frequency changes by the square root of the inverse of that, which is 3.
The new frequency is 120 x 3 = 360 kHz. The commonest slip is to use the capacitance ratio itself rather than its square root, which would give a frequency that is wrong by a factor of the square root.
Common mistakes
- 40/3 is not the answer: 40/3
- 720 is not the answer: 720
- 40 is not the answer: 40
Question 4
A capacitor of 10 uF and a resistor of 100 k form a timing circuit. What is its time constant, in milliseconds?
-
A
1
-
B
1000
-
C
110
-
D
1000000
Answer: Option B — with explanation
The time constant of a capacitor charging through a resistor is the product of the two: tau = R C. It is the time in which the capacitor reaches about 63 per cent of the supply voltage, and about five of them are needed to call it fully charged.
A resistance in kilohms and a capacitance in microfarads multiply to a time in milliseconds, which is what is asked for: 100 x 10 = 1000 ms.
Converting one of the two without the other is the usual slip - working in ohms and farads would give the answer in seconds, and it would be a thousand times too small as a number of milliseconds. The product rule needs no conversion at all as long as the units are a matched pair of this kind.
Common mistakes
- 110 is not the answer: 110
- 1 is not the answer: 1
- 1000000 is not the answer: 1000000
Question 5
An amplitude modulated wave has a carrier of 40 V and the modulating signal has a peak of 12 V. What is the modulation index?
-
A
0.30
-
B
0.70
-
C
3.33
-
D
1.30
Answer: Option A — with explanation
The modulation index is the peak of the modulating signal divided by the carrier amplitude. It says how far the carrier is pushed up and down, as a fraction of its own height.
That is 12 / 40 = 0.30.
An index of one is the most a carrier can take without the envelope cutting off, and anything above one is over modulation. An index above one, or a ratio of the carrier to the signal rather than the signal to the carrier, is what the other answers are built on.
Common mistakes
- 0.70 is not the answer: 0.70
- 3.33 is not the answer: 3.33
- 1.30 is not the answer: 1.30
Frequently asked questions
How do I remember whether a decibel question wants 10 or 20?
Look at what the ratio is of. Powers take 10, voltages and currents take 20. The factor of two is there because power goes as the square of voltage, so the logarithm of a power is twice the logarithm of the voltage.
Why is the gain of a non-inverting amplifier never less than one?
Because the input goes straight into the non-inverting terminal and the feedback only adds to it. The output is always at least as large as the input, and the one in the formula is what carries that minimum.
Do I have to convert kilohms and microfarads before multiplying?
Not if the answer is wanted in milliseconds. A resistance in kilohms and a capacitance in microfarads multiply to milliseconds exactly because the two factors of a thousand cancel. Convert only if the question asks for seconds.
What is the difference between the average and the root mean square value?
The average is the plain arithmetic mean of the wave over a cycle, and it is what a moving coil meter shows. The root mean square is the value that produces the same heating in a resistor, and it is what matters for power. For a sine they differ by about ten per cent.
Why does the flow through an orifice plate not double when the differential doubles?
Because the differential is the energy that the plate converts into motion, and kinetic energy goes as the square of the speed. To double the flow you need four times the differential, so the flow goes as the square root of it.
What happens if I sample a signal too slowly?
The frequencies above half the sampling rate fold back into the band as aliases - a tone that was never in the signal appears, and it cannot be told apart from a real one afterwards. Filtering before the converter is the only cure.
