Push-Pull Power Amplifiers¶

Possible Exam Questions¶

1. Definition and Need¶

A push-pull amplifier uses two active devices so that their output contributions have opposite current directions and combine in the load. In Class B, one device handles the positive half-cycle and the other the negative half-cycle.

Push-pull operation is used because it:

• delivers both halves of a high-power waveform;
• gives much higher ideal efficiency than Class A;
• ideally draws no quiescent Class-B output current;
• can cancel even-order distortion and DC magnetisation in a symmetric transformer primary;
• permits impedance matching or transformerless complementary output.

2. Class A, B and AB Bias¶

Push-pull can be Class A, but Class B/AB is normally chosen for output power. Class-AB efficiency is signal-dependent: it lies between corresponding Class-A and Class-B behaviour and approaches the Class-B limit at large output; it is not a fixed \(50\)–\(78.5\%\) for every signal level.

3. Complementary-Symmetry Class B¶

Complementary symmetry uses matched NPN/PNP BJTs (or NMOS/PMOS devices) in emitter/source-follower form and does not require an output transformer.

Positive Half-Cycle¶

• NPN \(Q_N\) is forward biased and sources load current.
• PNP \(Q_P\) is off.
• The output follows the positive input excursion, less device headroom.

Negative Half-Cycle¶

• PNP \(Q_P\) is forward biased and sinks load current toward the negative rail.
• NPN \(Q_N\) is off.
• The output follows the negative excursion.

The load receives the reconstructed full cycle. “Complementary” refers to opposite-polarity devices with corresponding characteristics; “symmetry” means the two paths should behave as nearly alike as practical.

4. Transformer-Coupled Class B¶

Two same-polarity transistors may instead be driven \(180^\circ\) apart by a centre-tapped input transformer. Their collector currents flow in alternate halves of a centre-tapped output-transformer primary; the secondary combines the flux changes and drives \(R_L\).

Transformer vs Complementary Form¶

5. Class-B Power and Efficiency¶

For an ideal complementary stage with symmetric \(\pm V_{CC}\) rails,

The load power is

Each rail supplies a half-wave current with average \(I_p/\pi\), so total DC input power is

Therefore

At the ideal maximum \(V_p=V_{CC}\),

Practical swing and efficiency are lower because of saturation/dropout voltage, bias current, driver loss, finite transistor gain and load/transformer loss.

6. Device Heat Dissipation¶

Total output-device dissipation is

For symmetric devices, average dissipation per transistor is

Differentiating with respect to \(V_p\) shows maximum per-device dissipation occurs at

This is below full output. A heat sink must therefore be designed for the worst device dissipation, not merely the maximum load power point.

7. Crossover Distortion¶

A silicon BJT needs roughly \(0.6\)–\(0.7\,\text{V}\) \(V_{BE}\) for substantial conduction. Around zero input,

neither ideal Class-B device conducts. The output develops a notch/dead band at every zero crossing, producing especially objectionable odd harmonics at small signal level.

8. Class-AB Remedy and Thermal Stability¶

Apply approximately \(2V_{BE}\) between complementary bases using two forward-biased diodes or an adjustable \(V_{BE}\) multiplier. Both devices then carry a small quiescent current and their transfer curves overlap.

Thermal design is essential because BJT \(V_{BE}\) falls by roughly \(2\,\text{mV}/^\circ\text{C}\) at a given current. Heating can otherwise raise current, causing more heating and possible thermal runaway.

Practical controls are:

• thermally couple bias diodes/\(V_{BE}\) multiplier to the output devices;
• use small emitter resistors for local current feedback and sharing;
• set and verify quiescent current after warm-up;
• provide an adequate heat sink and, where needed, current/temperature protection.

Too little bias leaves crossover distortion; too much causes excessive idle dissipation or simultaneous-conduction (shoot-through) current.

9. Advantages, Disadvantages and Applications¶

Advantages¶

• high ideal Class-B efficiency;
• little ideal no-signal dissipation;
• large AC load power;
• even-harmonic and supply-ripple cancellation when paths are symmetric;
• complementary form needs no output transformer.

Disadvantages¶

• Class B has crossover distortion;
• Class AB needs accurate, thermally tracked bias;
• matched complementary devices and driver current may be required;
• transformer form is bulky, costly and bandwidth-limited;
• short-circuit and thermal protection are important at power level.

Applications¶

Audio power amplifiers, loudspeaker/headphone drivers, servo and actuator drivers, RF linear stages (with suitable tuned/load networks) and transmitter power stages.

Rapid Recall¶

• Positive half: upper/NPN path conducts.
• Negative half: lower/PNP or second transformer-driven path conducts.
• \(P_L=V_p^2/(2R_L)\).
• \(P_{DC}=2V_{CC}V_p/(\pi R_L)\).
• \(\eta_{max}=\pi/4\).
• Cure crossover with thermally tracked Class-AB bias.

Model Answer — Class-B Push-Pull Operation and Efficiency [10 marks]¶

Exam-ready answer

A Class-B push-pull amplifier uses two devices biased at cutoff, each conducting for \(180^\circ\). One supplies the positive load-current half-cycle and the other supplies the negative half-cycle. This uses supply power more efficiently than Class A and reconstructs a full load waveform.

In complementary symmetry, positive input forward-biases the NPN, which sources current through \(R_L\), while the PNP is off. Negative input forward-biases the PNP, which sinks current, while the NPN is off. In transformer coupling, a centre-tapped input secondary drives two same-polarity transistors in antiphase; alternate collector currents excite opposite halves of a centre-tapped output primary and the secondary combines them.

For symmetric \(\pm V_{CC}\) supplies and sinusoidal output peak \(V_p\),

\[ I_p=\frac{V_p}{R_L},\qquad P_L=\frac{V_p^2}{2R_L}. \]

Each supply carries a half-wave current whose average is \(I_p/\pi\), hence

\[ P_{DC}=2V_{CC}\frac{I_p}{\pi} =\frac{2V_{CC}V_p}{\pi R_L}. \]

Therefore

\[ \eta=\frac{P_L}{P_{DC}} =\frac{\pi}{4}\frac{V_p}{V_{CC}} \le\boxed{\frac\pi4=78.5\%}. \]

The ideal maximum load power is \(V_{CC}^2/(2R_L)\). Device dissipation is \(P_{DC}-P_L\); per transistor it is maximised at \(V_p=2V_{CC}/\pi\), where \(P_{D(max)}=V_{CC}^2/(\pi^2R_L)\), not at full output.

Advantages are high efficiency, low ideal idle loss, large output and cancellation in a symmetric pair. Limitations are crossover distortion, thermal/bias control, device matching and protection; transformers additionally add bulk, loss and restricted bandwidth. Uses include audio, servo and transmitter power stages.

Practice target: 18 minutes; draw one complementary and one transformer form, trace both half-cycles, derive \(P_L\), \(P_{DC}\) and \(\pi/4\), then state the dissipation trap.

Model Answer — Crossover Distortion, Class AB and Thermal Stability [5 marks]¶

Exam-ready answer

Crossover distortion is the zero-crossing notch in an unbiased complementary Class-B stage. A silicon transistor needs about \(0.6\)–\(0.7\,\text{V}\) \(V_{BE}\), so for approximately \(-V_{BE}<v_i<+V_{BE}\) neither output transistor carries appreciable current. The load voltage becomes flat or discontinuous near zero and gains odd harmonics.

Class AB applies approximately \(2V_{BE}\) between the bases with two forward diodes or a \(V_{BE}\) multiplier. A small quiescent current then keeps both devices just conducting at zero, and each conducts slightly more than \(180^\circ\) so their transfer curves overlap.

Bias must track temperature. As a BJT heats, \(V_{BE}\) falls, which can increase current and cause thermal runaway. Bias diodes or the \(V_{BE}\) multiplier are thermally coupled to the output devices; emitter resistors add current feedback and aid sharing; a heat sink and current/temperature protection remove and limit heat. Too little bias leaves a notch, while too much causes high idle loss or shoot-through.

Practice target: 8 minutes; draw the dead zone and two-diode remedy, then state the too-little/too-much-bias consequences and three thermal controls.