Electronics (A-level only)

State the condition involving $V_{\mathrm{GS}}$ and $V_{\mathrm{th}}$ for an enhancement-mode n-channel MOSFET to begin conducting.

A $9.0\,\text{V}$ moisture alarm has a sensor of resistance $R$ from the positive supply to a MOSFET gate and a $1.5\,\text{M}\Omega$ resistor from the gate to $0\,\text{V}$. The MOSFET threshold voltage is $3.0\,\text{V}$. Determine $R$ when the MOSFET first switches on.

A MOSFET controls a $150\,\Omega$ load from a $12.0\,\text{V}$ supply. At the applied gate voltage its output characteristic is approximated by $I_{\mathrm{D}}=65\,\text{mA}$ for $V_{\mathrm{DS}}\geq2.0\,\text{V}$. Use load-line reasoning to determine the operating values of $V_{\mathrm{DS}}$, load power and MOSFET power. Deduce whether the MOSFET is acting as an efficient fully-on switch.

State the bias direction and operating region used when a Zener diode provides a constant-voltage reference.

A no-load voltage reference uses a $5.6\,\text{V}$ Zener diode on a $12.0\,\text{V}$ supply. Calculate the series resistance required for a Zener current of $16\,\text{mA}$.

A $6.2\,\text{V}$ Zener circuit is supplied from a fixed $14.0\,\text{V}$ source. The parallel load can draw up to $18\,\text{mA}$ and the Zener needs at least $5.0\,\text{mA}$. Determine the largest suitable series resistor from $330\,\Omega$, $360\,\Omega$ and $390\,\Omega$, and then determine minimum safe power ratings for the resistor and Zener when the load is disconnected.

Name the operating mode of a photodiode that has an external reverse-bias voltage.

A photodiode has responsivity $0.42\,\text{A W}^{-1}$ at the wavelength used. Radiation of power $8.0\,\mu\text{W}$ reaches it and its photocurrent passes through a $180\,\text{k}\Omega$ resistor. Calculate the magnitude of the resistor voltage.

A particle deposits energy in a scintillator, producing a $25\,\text{ns}$ optical pulse of constant power $4.0\,\mu\text{W}$. A reverse-biased photodiode has responsivity $0.48\,\text{A W}^{-1}$ and its readout converts the photocurrent using $270\,\text{k}\Omega$. Explain how the particle is detected, then calculate the voltage-pulse magnitude and the number of charge carriers in the photocurrent. Use $e=1.60\times10^{-19}\,\text{C}$.

The magnetic flux density through a Hall element doubles without changing its current or orientation. State the effect on its Hall voltage.

A Hall sensor has a zero-field output of $2.500\,\text{V}$ and sensitivity $45\,\text{mV T}^{-1}$. Calculate its output for a flux density of $-0.18\,\text{T}$.

A Hall sensor's output changes by $0.180\,\text{V}$ in a calibration field of $60\,\text{mT}$. In a speed monitor its peak output change is $0.120\,\text{V}$. Six identical magnets on a wheel each produce one pulse, and the pulse frequency is $180\,\text{Hz}$. Determine the peak magnetic flux density at the sensor and the wheel speed in revolutions per minute. Explain how the field calculation uses the Hall effect.

State one difference between an analogue signal and a binary digital signal.

An $8$-bit converter divides an input range from $0$ to $4.8\,\text{V}$ into equal quantisation intervals. Calculate the interval width and the maximum quantisation error.

A sensor signal contains frequencies up to $4.0\,\text{kHz}$. It is sampled at $10\,\text{kHz}$ with $14$ bits per sample for $45\,\text{s}$. Explain whether the sampling rate is sufficient, calculate the uncompressed data size in bits and bytes, and discuss one consequence of reducing the resolution to $8$ bits.

Calculate the resonant frequency of an LC filter containing $L=2.0\,\text{mH}$ and $C=8.0\,\text{nF}$.

A tuned circuit has a response peak at $150\,\text{kHz}$. Its lower and upper half-power frequencies are $143\,\text{kHz}$ and $157\,\text{kHz}$. Determine its bandwidth and Q-factor.

A receiver uses a $0.75\,\text{mH}$ inductor in an LC filter tuned to $620\,\text{kHz}$. Its measured half-power frequencies are $609\,\text{kHz}$ and $631\,\text{kHz}$. Calculate the required capacitance and Q-factor. The wanted transmission occupies $18\,\text{kHz}$ centred on resonance; discuss whether the measured bandwidth is suitable.

State the current entering either input terminal of an ideal operational amplifier.

An ideal operational amplifier has negative feedback, its non-inverting input is connected to $0\,\text{V}$, and its output is not saturated. State the potential of the inverting input and explain why that point is called a virtual earth.

The non-inverting terminal of an ideal op amp is earthed. A $+0.80\,\text{V}$ source is connected to the inverting node through $40\,\text{k}\Omega$, and negative feedback connects the output to that node through $200\,\text{k}\Omega$. The supply rails are $\pm6.0\,\text{V}$. Use the ideal-op-amp rules to determine the output voltage and verify that the assumed linear operation is possible.

An inverting amplifier has $R_{\text{in}}=10\,\text{k}\Omega$, $R_f=47\,\text{k}\Omega$ and $V_{\text{in}}=+0.60\,\text{V}$. Calculate $V_{\text{out}}$.

The non-inverting input of an ideal operational amplifier is earthed. Its input and feedback resistors are $12\,\text{k}\Omega$ and $68\,\text{k}\Omega$. Derive the closed-loop gain from currents at the inverting input, then determine the output for $V_{\text{in}}=-0.45\,\text{V}$.

An inverting amplifier has $R_{\text{in}}=15\,\text{k}\Omega$ and $R_f=120\,\text{k}\Omega$. Its output saturates at $\pm8.0\,\text{V}$. A sinusoidal input has peak voltage $1.4\,\text{V}$. Determine the ideal output peak, describe the actual output, and calculate the largest input peak that would avoid clipping.

A non-inverting amplifier has $R_1=10\,\text{k}\Omega$, $R_f=39\,\text{k}\Omega$ and input voltage $0.80\,\text{V}$. Calculate its output voltage.

In a non-inverting amplifier, $R_1=8.2\,\text{k}\Omega$ joins the inverting input to earth and $R_f=33\,\text{k}\Omega$ joins the output to that input. Use the feedback-divider potential to derive the gain and calculate the output when $V_{\text{in}}=0.50\,\text{V}$.

A non-inverting amplifier uses $R_1=18\,\text{k}\Omega$ and $R_f=82\,\text{k}\Omega$. Its output saturates at $\pm11.5\,\text{V}$. Calculate the maximum peak-to-peak sinusoidal input that can be amplified without clipping, and state the corresponding output peak-to-peak voltage.

A summing amplifier has $R_f=20\,\text{k}\Omega$. Two inputs of $0.30\,\text{V}$ and $0.50\,\text{V}$ are each connected through $10\,\text{k}\Omega$. Calculate the output voltage.

A summing amplifier has $R_f=60\,\text{k}\Omega$. Inputs $+0.90\,\text{V}$, $-1.20\,\text{V}$ and $+0.50\,\text{V}$ are connected through $15\,\text{k}\Omega$, $30\,\text{k}\Omega$ and $20\,\text{k}\Omega$, respectively. Determine $V_{\text{out}}$.

A summing amplifier has $R_f=100\,\text{k}\Omega$ and saturates at $-10.5\,\text{V}$ on negative output. Inputs $+1.20\,\text{V}$, $-0.60\,\text{V}$ and $+1.50\,\text{V}$ pass through $12\,\text{k}\Omega$, $30\,\text{k}\Omega$ and $20\,\text{k}\Omega$. Calculate the ideal output, state the actual output, and find the value to which the third input must be reduced to put the amplifier just at the saturation boundary.

An operational amplifier has a gain--bandwidth product of $3.0\,\text{MHz}$. Calculate its bandwidth when its closed-loop voltage gain is $30$.

A real operational amplifier has slew rate $1.5\,\text{V}\,\mu\text{s}^{-1}$. Determine whether it can produce an undistorted sine wave of frequency $80\,\text{kHz}$ and peak output $4.0\,\text{V}$. Also calculate the greatest frequency allowed by the slew rate at this peak voltage.

An operational amplifier has gain--bandwidth product $4.0\,\text{MHz}$ and slew rate $0.80\,\text{V}\,\mu\text{s}^{-1}$. It is used at closed-loop gain $25$ to produce a $60\,\text{kHz}$ sine wave whose ideal output peak is $3.0\,\text{V}$. Test both frequency limitations and calculate the largest undistorted output peak at this frequency.

For the Boolean function $Y=A\cdot\overline{B}$, state the four values of $Y$ for inputs $AB=00,01,10,11$ in that order.

A two-input circuit must output $1$ for $AB=01$ and $AB=10$, but $0$ for $AB=00$ and $AB=11$. Identify the single gate that performs this function and write an equivalent Boolean expression using only AND, OR and NOT.

A control output is $Y=(A+B)\cdot\overline{C}$. Construct its eight-row truth-table output with $ABC$ in ascending binary order from $000$ to $111$, then describe a NAND-only implementation.

A three-bit up-counter is reset to $000$. State its output after five clock pulses, writing the most significant bit first.

State the number of distinct states of a four-stage Johnson counter and of a four-bit BCD counter. A BCD counter receives a $1.20\,\text{kHz}$ clock; determine the rate at which it completes full count cycles.

A three-bit up-counter is converted to a modulo-$6$ counter by decoding one state to reset it. Identify the decoded reset state, list the stable count sequence, determine the output after $53$ pulses from reset, and calculate the cycle rate for a $24\,\text{kHz}$ clock.

An astable produces a pulse train of period $2.5\,\text{ms}$ with a high pulse lasting $1.0\,\text{ms}$. Calculate the frequency and duty cycle.

In an astable, a capacitor charges through $47\,\text{k}\Omega$ from $V_S/3$ to $2V_S/3$ and then discharges through the same resistance over the reverse threshold interval. The capacitance is $22\,\text{nF}$. Using exponential charging, determine the period and frequency.

An astable capacitor switches between $V_S/3$ and $2V_S/3$, with the output high while the capacitor charges. It charges through $82\,\text{k}\Omega$, discharges through $33\,\text{k}\Omega$, and has capacitance $15\,\text{nF}$. Calculate the high time, low time, frequency, duty cycle and mark-to-space ratio, taking each threshold time as $RC\ln2$.

Place these stages of a real-time communication system in order: receiver, output transducer, transmission channel, input transducer, transmitter.

In a live radio link, explain the different purposes of the transmitter, transmission channel and receiver.

A remote weather station sends a continuously updated temperature reading to a control room. Describe a complete real-time communication system for this task, giving the purpose of each block and explaining where unwanted noise can affect the recovered reading.

Identify a suitable transmission medium for a high-data-rate link that should be difficult to intercept, and give one reason for your choice.

Explain two ways in which a radio transmission can reach a receiver beyond the horizon, and relate each way to the wave behaviour involved.

A signal travels from one ground station to another through a geostationary satellite $3.60\times10^7\,\text{m}$ above Earth. Treat both path sections as vertical and use $c=3.00\times10^8\,\text{m s}^{-1}$. Calculate the minimum one-way delay, explain why uplink and downlink frequencies differ, and compare this link with optical fibre for data rate and security.

Four channels share a time-division multiplexed link. Each frame contains one $8$-bit slot from every channel. State the number of slots and the number of data bits in one frame.

Six signals are each sampled at $8.0\,\text{kHz}$ and represented by $10$ bits per sample. One sample from each signal forms a TDM frame with no overhead. Calculate the frame rate, slot rate and transmitted bit rate.

A TDM system carries $24$ channels, each sampled at $12.0\,\text{kHz}$ with $12$ bits per sample. Every frame also contains $8$ synchronisation bits. Calculate the frame rate, data-slot rate, total bits per frame and transmitted bit rate. Decide whether a $4.00\,\text{Mbit s}^{-1}$ link has sufficient capacity.

An AM transmission carries a highest information frequency of $6.0\,\text{kHz}$. Calculate its minimum bandwidth.

A signal with maximum information frequency $8.0\,\text{kHz}$ frequency-modulates a carrier with maximum deviation $25\,\text{kHz}$. Calculate the FM bandwidth and the bandwidth if the same information used AM.

A broadcast signal has maximum information frequency $15\,\text{kHz}$. In FM its maximum frequency deviation is $75\,\text{kHz}$. Calculate the FM and AM bandwidths and hence the greatest ideal number of non-overlapping channels of each type in a $900\,\text{kHz}$ allocation. Explain one signal-to-noise advantage and one channel-usage disadvantage of FM.