Electronic devices and analog circuits

What to remember

• A PN junction conducts easily in forward bias and almost not at all in reverse bias; a BJT is a current-controlled device, a FET is a voltage-controlled device.
• Negative feedback stabilises gain and widens bandwidth; positive feedback with loop gain Aβ = 1 and zero phase shift makes an oscillator.
• An ideal op-amp has infinite gain, infinite input resistance, zero output resistance and infinite bandwidth; with negative feedback the two inputs are at the same voltage (virtual short).

Semiconductor basics

Silicon and germanium are Group IV elements. Pure material is called intrinsic. Doping with a Group V atom (phosphorus, arsenic) gives n-type material: electrons are the majority carriers. Doping with a Group III atom (boron, gallium) gives p-type material: holes are the majority carriers.

In any semiconductor in thermal equilibrium, the mass-action law holds: n × p = ni². Here ni is the intrinsic carrier concentration. For an n-type sample, n ≈ ND, so p = ni²/ND.

Energy gap at room temperature: silicon about 1.1 eV, germanium about 0.67 eV. Conductivity σ = q(nμn + pμp). The resistivity of a semiconductor falls as temperature rises (negative temperature coefficient).

Two current mechanisms: drift (due to electric field) and diffusion (due to concentration gradient). The Einstein relation gives D/μ = VT, where VT = kT/q, about 26 mV at 300 K.

PN junction diode

At the junction, a depletion region forms with no free carriers. A built-in potential (barrier) exists: about 0.7 V for silicon and 0.3 V for germanium. Forward bias narrows the depletion region; reverse bias widens it.

Diode equation: I = I0 (e^(V/ηVT) − 1). The reverse saturation current I0 roughly doubles for every 10 °C rise. The forward voltage drop falls by about 2 mV per °C.

Capacitances: reverse bias gives transition (depletion) capacitance; forward bias gives diffusion capacitance. A varactor diode uses the transition capacitance as a voltage-variable capacitor.

Breakdown: Zener breakdown happens in heavily doped junctions with narrow depletion layers (below about 5 V). Avalanche breakdown happens in lightly doped junctions (above about 7 V). Zener diodes work in reverse breakdown as voltage regulators. Other diodes: LED (light emission on forward bias), photodiode (reverse biased, current rises with light), Schottky diode (metal-semiconductor, fast switching, low drop), tunnel diode (negative resistance region).

Rectifiers and filters

A bridge uses four diodes. A capacitor filter reduces ripple; ripple falls as the capacitance and load resistance rise. A Zener shunt regulator keeps the load voltage nearly constant while the Zener stays in breakdown.

Bipolar junction transistor (BJT)

Two junctions, three regions: emitter (heavily doped), base (thin, lightly doped), collector. Relations: IE = IB + IC; α = IC/IE; β = IC/IB; β = α/(1 − α); α = β/(1 + β).

Configurations: common-base (current gain about 1, low input resistance), common-emitter (high voltage and current gain, phase shift 180°), common-collector or emitter follower (voltage gain about 1, high input resistance, low output resistance, used as a buffer).

Biasing fixes the Q-point. Fixed bias is poorly stable; voltage-divider bias gives the best stability. Thermal runaway is a danger because ICBO rises with temperature. Small-signal model: gm = IC/VT; rπ = β/gm.

Amplifier classes: Class A conducts for 360° (efficiency max 25 % with resistive load, 50 % with transformer coupling); Class B conducts for 180° (max 78.5 %); Class AB sits between them and removes crossover distortion; Class C conducts for less than 180° and is used in tuned RF amplifiers.

Field-effect transistors

A JFET has a channel controlled by the reverse-biased gate junction. Pinch-off voltage VP is the gate-source voltage where the channel closes. In saturation, ID = IDSS (1 − VGS/VP)². Transconductance gm = 2IDSS/|VP| × (1 − VGS/VP).

A MOSFET has an insulated gate, so the input resistance is extremely high. Enhancement-mode devices conduct only after VGS exceeds the threshold voltage VT. Saturation current: ID = (K/2)(VGS − VT)². Depletion-mode devices conduct at VGS = 0. CMOS pairs an n-MOS and a p-MOS device and uses very little static power.

Feedback and oscillators

Gain with feedback: Af = A/(1 + Aβ) for negative feedback. Negative feedback desensitises gain, increases bandwidth, lowers distortion and noise. Series mixing raises input resistance; shunt mixing lowers it. Voltage sampling lowers output resistance; current sampling raises it.

Barkhausen criterion: |Aβ| = 1 and total loop phase shift 0° (or 360°). RC phase-shift oscillator: f = 1/(2πRC√6), needs gain of at least 29. Wien bridge: f = 1/(2πRC), needs gain of 3. Hartley uses two inductors; Colpitts uses two capacitors; crystal oscillators give high frequency stability because of the high Q factor.

Operational amplifiers

Inverting amplifier: gain = −Rf/R1. Non-inverting: gain = 1 + Rf/R1. Voltage follower: gain 1. Summer: Vo = −Rf(V1/R1 + V2/R2 + …). Integrator: Vo = −(1/RC)∫Vin dt. Differentiator: Vo = −RC dVin/dt. Common-mode rejection ratio (CMRR) = Ad/Ac should be high. Slew rate is the maximum rate of change of output (V/µs). Gain-bandwidth product is constant for a single-pole op-amp. Comparator: op-amp without feedback; Schmitt trigger: comparator with positive feedback (hysteresis).

Worked examples

• 1. A transistor has β = 99. Then α = 99/100 = 0.99. If IB = 20 µA, IC = 99 × 20 = 1.98 mA.
• 2. Peak input 10 V to a half-wave rectifier: Vdc = 10/π ≈ 3.18 V.
• 3. An inverting op-amp with R1 = 10 kΩ and Rf = 100 kΩ has gain −10; for Vin = 0.5 V, Vo = −5 V.
• 4. Wien bridge with R = 10 kΩ, C = 0.01 µF: f = 1/(2π × 10⁴ × 10⁻⁸) ≈ 1.59 kHz.

Special-purpose devices and switching

An LED is made from direct-gap compound semiconductors such as gallium arsenide and gallium phosphide; silicon is not used because it is an indirect-gap material and gives very little light. A photodiode works in reverse bias, and its reverse current rises with light intensity. A solar cell works without external bias and converts light into electrical power. An optocoupler joins an LED and a photodetector and gives electrical isolation between two circuits.

A thyristor (SCR) has four layers, PNPN, and three terminals: anode, cathode and gate. It stays off until a gate pulse triggers it. After triggering it stays on until the anode current falls below the holding current. A TRIAC conducts in both directions and is used for AC power control. A UJT is used in relaxation oscillators and as a firing circuit for SCRs.

A transistor switch has two states. In cut-off the output is near the supply voltage. In saturation the collector-emitter voltage is very small, about 0.2 V. Switching speed is limited by storage time and by junction capacitances.

Frequency response and coupling

In a multistage amplifier, RC coupling gives a flat mid-band gain. At low frequencies, gain falls because of coupling and bypass capacitors. At high frequencies, gain falls because of junction and stray capacitances. The half-power frequencies f1 and f2 are the points where gain falls to 0.707 of the mid-band value, which is 3 dB down. Bandwidth = f2 − f1. Gain in decibels = 20 log10(Vo/Vi) for voltage and 10 log10(Po/Pi) for power. A transformer-coupled stage gives good impedance matching. A direct-coupled (DC) amplifier can amplify DC signals but suffers from drift. A differential amplifier gives a large output for the difference of two inputs and a small output for a common signal; a long-tailed pair with a constant-current source gives a high CMRR.

Power supplies

A regulated supply has a rectifier, a filter and a regulator. Line regulation is the change in output voltage for a change in input voltage. Load regulation is the change in output voltage from no-load to full-load, expressed as a percentage of full-load voltage. The 78xx series gives fixed positive voltages and the 79xx series gives fixed negative voltages; for example, 7805 gives +5 V. The LM317 gives an adjustable positive output. A series pass transistor regulator is more efficient than a simple Zener regulator for large loads. A switching regulator uses a transistor as a switch with a high duty-cycle control and gives higher efficiency than a linear regulator.

Exam traps

• Zener breakdown (low voltage, heavy doping) versus avalanche (high voltage, light doping).
• Bridge rectifier PIV is Vm; centre-tap PIV is 2Vm.
• Ripple frequency in full-wave is 2f, not f.
• Transition capacitance is in reverse bias; diffusion capacitance is in forward bias.
• Class B maximum efficiency 78.5 %, Class A 25 % (resistive load).
• BJT is current-controlled; FET is voltage-controlled and unipolar.
• Common-collector has no voltage gain even though it has high current gain.
• Wien bridge needs gain 3; phase-shift oscillator needs gain 29.

One-liners

• 1. n × p = ni² in equilibrium.
• 2. Silicon barrier about 0.7 V; germanium about 0.3 V.
• 3. Thermal voltage VT is about 26 mV at room temperature.
• 4. Half-wave ripple factor is 1.21; full-wave is 0.482.
• 5. β = α/(1 − α).
• 6. Emitter follower is the buffer stage.
• 7. Active mode: emitter junction forward, collector junction reverse.
• 8. MOSFET has the highest input resistance among the common devices.
• 9. Barkhausen: loop gain 1, phase 0°.
• 10. Virtual short exists in negative-feedback op-amp circuits.
• 11. Schottky diode is the fast-switching diode.
• 12. Crystal oscillator gives the best frequency stability.

Practice questions

1. Doping silicon with phosphorus produces which type of material?

   1. n-type, with holes as majority carriers
   2. Intrinsic material with equal carriers
   3. p-type, with holes as majority carriers
   4. n-type, with electrons as majority carriers
   Answer

   D. n-type, with electrons as majority carriers

   Phosphorus is Group V, a donor, so electrons are the majority carriers.

2. In a semiconductor in thermal equilibrium, the product of electron and hole concentrations equals

   1. ni cubed
   2. ni squared
   3. ni
   4. ni divided by two
   Answer

   B. ni squared

   Mass-action law: n·p = ni².

3. The approximate cut-in (barrier) voltage of a silicon PN diode is

   1. 0.3 V
   2. 0.1 V
   3. 0.7 V
   4. 1.2 V
   Answer

   C. 0.7 V

   Silicon about 0.7 V; germanium about 0.3 V.

4. Which diode is normally operated in reverse breakdown as a voltage regulator?

   1. Varactor diode
   2. Zener diode
   3. Schottky diode
   4. Tunnel diode
   Answer

   B. Zener diode

   Zener diodes hold a nearly constant voltage in breakdown.

5. An n-type sample has donor concentration 10^16 per cm³ and ni² = 10^20 (cm⁻³)². The hole concentration is

   1. 10^16 per cm³
   2. 10^-4 per cm³
   3. 10^36 per cm³
   4. 10^4 per cm³
   Answer

   D. 10^4 per cm³

   p = ni²/n = 10^20/10^16 = 10^4.

6. The ripple factor of an ideal half-wave rectifier is

   1. 0.812
   2. 0.406
   3. 1.21
   4. 0.482
   Answer

   C. 1.21

   Standard result: 1.21 for half-wave, 0.482 for full-wave.

7. A sinusoidal input of peak 20 V feeds a full-wave rectifier. Ignoring diode drops, the average output voltage is nearly

   1. 12.7 V
   2. 6.37 V
   3. 10 V
   4. 14.1 V
   Answer

   A. 12.7 V

   Vdc = 2Vm/π = 40/3.14 ≈ 12.7 V.

8. The peak inverse voltage of each diode in a centre-tap full-wave rectifier with secondary peak Vm (each half) is

   1. 2Vm
   2. Vm
   3. Vm/π
   4. Vm/2
   Answer

   A. 2Vm

   Each off-state diode sees both half-windings: 2Vm.

9. The maximum rectification efficiency of a half-wave rectifier is

   1. 50 %
   2. 78.5 %
   3. 81.2 %
   4. 40.6 %
   Answer

   D. 40.6 %

   Half-wave maximum efficiency is 40.6 %; full-wave 81.2 %.

10. Capacitance that dominates in a forward-biased PN junction is

    1. depletion capacitance
    2. stray wiring capacitance
    3. diffusion capacitance
    4. transition capacitance
    Answer

    C. diffusion capacitance

    Forward bias stores minority charge; diffusion capacitance dominates. Transition is for reverse bias.

11. A BJT has α = 0.98. Its β is

    1. 98
    2. 49
    3. 0.02
    4. 50.5
    Answer

    B. 49

    β = α/(1 − α) = 0.98/0.02 = 49.

12. A transistor has β = 100 and IB = 30 µA. The emitter current is

    1. 3.00 mA
    2. 0.303 mA
    3. 3.03 mA
    4. 30.3 mA
    Answer

    C. 3.03 mA

    IC = 3 mA; IE = IC + IB = 3.03 mA.

13. For a BJT to act as a closed switch, it must be in

    1. saturation
    2. cut-off
    3. active region
    4. reverse active only
    Answer

    A. saturation

    Both junctions forward biased: saturation, switch ON.

14. Which BJT configuration is used as a buffer because of high input and low output resistance?

    1. Common emitter
    2. Common base
    3. Common collector
    4. Common emitter with emitter resistor only
    Answer

    C. Common collector

    Emitter follower: gain about 1, high Rin, low Rout.

15. The common-emitter amplifier gives a phase shift of

    1. 0°
    2. 180° between input and output
    3. 90°
    4. 270°
    Answer

    B. 180° between input and output

    CE amplifier inverts the signal.

16. Which biasing arrangement gives best Q-point stability?

    1. Fixed bias
    2. Collector-to-base bias with no resistor
    3. Base bias with very large RB
    4. Voltage-divider bias
    Answer

    D. Voltage-divider bias

    Voltage-divider bias with emitter resistor is least sensitive to β and temperature.

17. The maximum collector efficiency of an ideal Class B push-pull amplifier is

    1. 78.5 %
    2. 100 %
    3. 25 %
    4. 50 %
    Answer

    A. 78.5 %

    π/4 = 78.5 %.

18. Crossover distortion is removed in power amplifiers by using

    1. Fixed zero bias
    2. Class AB biasing
    3. Class C biasing
    4. Class A without feedback
    Answer

    B. Class AB biasing

    A small forward bias on both transistors in Class AB removes the dead zone.

19. A JFET has IDSS = 8 mA and VP = −4 V. At VGS = −2 V, the drain current in saturation is

    1. 4 mA
    2. 1 mA
    3. 6 mA
    4. 2 mA
    Answer

    D. 2 mA

    ID = 8(1 − 0.5)² = 8 × 0.25 = 2 mA.

20. In an n-channel enhancement MOSFET, current flows only when

    1. VGS is negative and large
    2. The drain is open
    3. VGS is zero
    4. VGS exceeds the threshold voltage
    Answer

    D. VGS exceeds the threshold voltage

    Channel is induced only above VT.

21. Which statement about MOSFET versus BJT is correct?

    1. MOSFET has much higher input resistance
    2. MOSFET is a current-controlled device
    3. MOSFET is a bipolar device
    4. MOSFET needs gate current for operation
    Answer

    A. MOSFET has much higher input resistance

    Insulated gate gives extremely high input resistance.

22. An amplifier has open-loop gain 1000 and negative feedback β = 0.09. The closed-loop gain is

    1. about 1000
    2. about 11
    3. about 111
    4. about 90
    Answer

    B. about 11

    Af = 1000/(1 + 90) = 10.99.

23. An amplifier of gain 100 uses negative feedback β = 0.1. By what factor does the gain fall?

    1. 1.1
    2. 100
    3. 11
    4. 10
    Answer

    C. 11

    1 + Aβ = 1 + 10 = 11, so gain = 100/11 ≈ 9.

24. Series-mixing negative feedback has the effect of

    1. making gain unstable
    2. increasing input resistance
    3. decreasing input resistance
    4. increasing output noise
    Answer

    B. increasing input resistance

    Series mixing raises Rin; shunt mixing lowers it.

25. Voltage-sampling negative feedback

    1. has no effect on output resistance
    2. makes the output current constant
    3. increases output resistance
    4. reduces output resistance
    Answer

    D. reduces output resistance

    Voltage sampling gives voltage-amplifier behaviour: low Rout.

26. An RC phase-shift oscillator (three stages) needs a minimum amplifier gain of

    1. 3
    2. 10
    3. 29
    4. 100
    Answer

    C. 29

    The three-stage RC network attenuates by 29.

27. The frequency of a Wien bridge oscillator with R = 1 kΩ and C = 0.1 µF is nearly

    1. 1.59 kHz
    2. 15.9 kHz
    3. 6.28 kHz
    4. 159 Hz
    Answer

    A. 1.59 kHz

    f = 1/(2πRC) = 1/(6.28 × 10⁻⁴) ≈ 1.59 kHz.

28. Which oscillator uses two capacitors and one inductor in its tank?

    1. Colpitts oscillator
    2. Wien bridge oscillator
    3. Hartley oscillator
    4. RC phase-shift oscillator
    Answer

    A. Colpitts oscillator

    Colpitts: capacitive divider; Hartley: inductive divider.

29. The best frequency stability among the oscillators is given by

    1. Hartley oscillator
    2. Colpitts oscillator
    3. Wien bridge oscillator
    4. crystal oscillator
    Answer

    D. crystal oscillator

    A quartz crystal has a very high Q.

30. An inverting op-amp has R1 = 5 kΩ and Rf = 50 kΩ. For an input of 0.2 V the output is

    1. −0.2 V
    2. −2 V
    3. +2 V
    4. +0.02 V
    Answer

    B. −2 V

    Gain = −Rf/R1 = −10; output = −2 V.

31. The gain of a non-inverting op-amp with R1 = 2 kΩ and Rf = 18 kΩ is

    1. −9
    2. −10
    3. 10
    4. 9
    Answer

    C. 10

    1 + Rf/R1 = 1 + 9 = 10.

32. The virtual short concept in an op-amp with negative feedback means

    1. the two inputs are at nearly the same voltage
    2. the output is shorted to ground
    3. the gain is zero
    4. the inputs draw large current
    Answer

    A. the two inputs are at nearly the same voltage

    With infinite gain, differential input must be near zero.

33. The op-amp circuit without feedback used to compare two voltages is the

    1. integrator
    2. summing amplifier
    3. voltage follower
    4. comparator
    Answer

    D. comparator

    Open-loop op-amp saturates according to input difference.

34. A Schmitt trigger uses

    1. positive feedback to give hysteresis
    2. negative feedback to give linear gain
    3. no feedback
    4. only capacitors
    Answer

    A. positive feedback to give hysteresis

    Positive feedback creates two threshold levels.

35. Slew rate of an op-amp is measured in

    1. Hz/V
    2. V/µs
    3. dB
    4. V/A
    Answer

    B. V/µs

    It is the maximum rate of output change.

36. An op-amp integrator has R = 100 kΩ and C = 1 µF. For a constant input of 1 V, the output slope magnitude is

    1. 0.1 V/s
    2. 1 V/s
    3. 10 V/s
    4. 100 V/s
    Answer

    C. 10 V/s

    |dVo/dt| = Vin/RC = 1/(0.1) = 10 V/s.

37. The reverse saturation current of a diode approximately

    1. is independent of temperature
    2. halves for every 10 °C rise
    3. doubles for every 10 °C rise
    4. doubles for every 1 °C rise
    Answer

    C. doubles for every 10 °C rise

    A standard rule of thumb for Si and Ge.

38. Which diode shows a negative-resistance region in its forward characteristic?

    1. Rectifier diode
    2. Zener diode
    3. LED
    4. Tunnel diode
    Answer

    D. Tunnel diode

    The tunnel diode has a negative-resistance dip.

39. Consider the statements. 1. A Zener diode regulates voltage in reverse breakdown. 2. An LED emits light when reverse biased. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    LEDs emit light under forward bias; statement 2 is false.

40. Consider the statements. 1. Negative feedback reduces distortion. 2. Negative feedback increases bandwidth. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are standard benefits, at the cost of gain.

41. Consider the statements. 1. In the active region the emitter-base junction is reverse biased. 2. In cut-off both junctions are reverse biased. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    Active mode needs a forward emitter junction; statement 1 is false.

42. Consider the statements. 1. JFET is a unipolar device. 2. A JFET gate junction is forward biased in normal operation. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    The JFET gate is reverse biased; only statement 1 is true.

43. Consider the statements about Barkhausen criterion. 1. Loop gain magnitude must be unity. 2. Total loop phase shift must be 0° or a multiple of 360°. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both conditions are required for sustained oscillation.

44. Match the oscillator with its feature: P. Wien bridge Q. Crystal R. Hartley 1. Two inductors 2. Gain of 3 3. High Q stability Choose the correct matching.

    1. P-3, Q-1, R-2
    2. P-2, Q-1, R-3
    3. P-1, Q-2, R-3
    4. P-2, Q-3, R-1
    Answer

    D. P-2, Q-3, R-1

    Wien bridge needs gain 3; crystal has high Q; Hartley has two inductors.

45. Match the rectifier with the ripple factor: P. Half-wave Q. Full-wave 1. 0.482 2. 1.21

    1. P-2, Q-2
    2. P-2, Q-1
    3. P-1, Q-2
    4. P-1, Q-1
    Answer

    B. P-2, Q-1

    Half-wave 1.21; full-wave 0.482.