Tuned Power Amplifiers¶

Possible Exam Questions¶

1. Definition and Need¶

A tuned amplifier uses a resonant network, normally an LC tank, as its collector/drain load. It gives high gain or output power in a narrow band around a selected frequency \(f_0\) while rejecting distant frequencies and harmonics. Its gain therefore has a band-pass response, so it is also called a band-pass amplifier. Unlike a passive band-pass filter, however, the active stage draws energy from a DC supply and provides power gain; the resonant load performs the frequency selection.

It is needed when a communication system must:

• select one carrier/channel;
• reject harmonics or adjacent-frequency energy;
• transform device current pulses into a near-sinusoidal RF voltage;
• obtain high RF power efficiency with a narrowband load.

“Tuned” describes the load response. A tuned stage can operate in Class A, AB, B or C. The familiar high-efficiency version is a Class-C tuned power amplifier.

2. Parallel LC Tank¶

For an ideal tank,

Resonance occurs when susceptances cancel:

At resonance, terminal impedance is maximum for a parallel tank, so a given collector-current fundamental produces maximum RF voltage. Energy alternates between capacitor electric field and inductor magnetic field; resistance and loading dissipate some energy each cycle.

3. Quality Factor and Bandwidth¶

The resistance model must be stated.

Parallel-Loss Model¶

For \(R_p\) directly in parallel with ideal \(L\) and \(C\),

Coil Series-Loss Model¶

If inductor loss is represented by small series resistance \(r_s\) and \(Q\gg1\),

The external load lowers the loaded quality factor:

Higher \(Q_L\) means narrower bandwidth and greater selectivity, but slower transient settling and greater sensitivity to component tolerance.

4. Collector-Tuned Class-C Circuit¶

Circuit Roles¶

• \(Q_1\) is biased below cutoff, so it conducts for less than \(180^\circ\).
• \(C_i\) couples RF drive while \(R_B\) establishes negative/cutoff bias.
• The RFC supplies DC but presents high impedance to RF, isolating the supply.
• Parallel \(L\)-\(C\) is the collector load and frequency selector.
• \(C_o\) couples RF output to \(R_L\) while blocking collector DC.

5. Working Through One Cycle¶

1. A sufficiently positive input excursion drives \(Q_1\) on briefly and injects a collector-current pulse into the tank.
2. The pulse contains a fundamental at the drive frequency plus harmonics.
3. If the tank is tuned to the fundamental, its impedance there is high; harmonic impedances are much lower or off-resonance, so harmonic voltage is suppressed.
4. During transistor-off time, stored tank energy continues to exchange between \(L\) and \(C\) and supplies the load.
5. Successive pulses replace tank and load losses, producing an approximately sinusoidal \(v_o\).

The transistor current itself remains pulsed; the tank voltage is sinusoidal. This distinction is central to the answer.

Why Class C Is Not a Linear Audio Stage¶

Without the tuned load, a Class-C stage reproduces only short portions of each input cycle and is severely nonlinear. A fixed high-\(Q\) tank can reconstruct one selected sinusoidal carrier, but an audio signal contains many simultaneous, time-varying frequency components. The tank would pass only a narrow part of that spectrum and reject the rest, changing the waveform and causing severe distortion. Class C is therefore used for tuned RF carrier and power stages, not for direct linear audio amplification.

6. Frequency Selectivity and Tuning¶

At \(f_0\), collector voltage and output are maximum. Moving away from resonance lowers tank impedance and gain. The half-power frequencies \(f_1,f_2\) bound the useful band.

Loading, transistor output capacitance and stray capacitance contribute to effective \(C\) and shift resonance. Practical RF stages therefore include adjustable capacitors/inductors or matching networks and are aligned under operating load.

7. Output Power and Efficiency¶

For sinusoidal RF voltage across an effective load \(R_L\),

DC input and collector efficiency are

Class C can reach high practical efficiency because transistor voltage and current overlap for a small portion of each cycle. Efficiency is not determined by conduction angle alone: saturation voltage, switching time, tank loss, RFC loss, device capacitance and matching all matter.

8. Tuned vs RC-Coupled and Direct-Coupled¶

Thus the tuned response is concentrated around one center frequency, the RC-coupled AC amplifier passes a broad band but blocks DC, and the direct-coupled DC amplifier retains gain down to zero frequency.

9. Types¶

• Single-tuned: one tank; simple and selective.
• Double-tuned: two coupled tanks; adjustable coupling trades bandwidth, flatness and skirt selectivity.
• Synchronously tuned: two or more cascaded stages are all tuned to the same \(f_0\); their gains multiply, giving a sharper, narrower composite response than one stage.
• Stagger-tuned: cascaded stages tuned to slightly different frequencies; wider, flatter composite passband.

Double-, synchronous- and stagger-tuned arrangements all use more than one resonator, but they shape the composite response differently.

Common High-Frequency Implementations¶

• Transformer-coupled tuned stages: coupled windings transfer RF, provide impedance transformation and can form a double-tuned network when both windings resonate.
• Cascode (CE-CB or CS-CG): the upper common-base/common-gate device reduces Miller feedback, improves reverse isolation and gives better high-frequency stability.
• CC-CB cascade: a common-collector buffer isolates the source or preceding resonator and supplies low-impedance drive to a common-base RF stage; the tuned load still sets the selected band.

10. Advantages, Disadvantages and Applications¶

Advantages¶

• high selectivity and harmonic rejection;
• high RF voltage gain at resonance;
• high efficiency in Class C;
• impedance transformation/matching can be incorporated;
• suitable for high-frequency transmitters and receivers.

Disadvantages¶

• narrowband and unsuitable for arbitrary broadband waveforms;
• component tolerance, temperature and loading detune the circuit;
• inductors can be bulky/lossy at low frequencies and parasitic at very high frequencies;
• alignment and shielding may be required;
• high tank voltage/current can stress components.

Applications¶

RF transmitters, radio communication power amplifiers, receiver RF/IF selection, frequency multipliers, oscillators and narrowband telemetry links.

Rapid Recall¶

• \(f_0=1/(2\pi\sqrt{LC})\).
• \(Q_L=f_0/BW\).
• Parallel tank: maximum \(Z\) at \(f_0\).
• Class C: conduction angle \(<180^\circ\).
• RFC passes DC and blocks RF from the supply.
• Synchronous tuning: same \(f_0\); stagger tuning: offset resonant frequencies.

Model Answer — Collector-Tuned Power Amplifier [10 marks]¶

Exam-ready answer

A collector-tuned power amplifier uses a parallel LC tank instead of a resistive collector load. Its purpose is to deliver power in a narrow RF band, reject harmonics and, in Class C, convert short transistor-current pulses into a sinusoidal tank voltage.

\(Q_1\) is biased below cutoff and conducts for less than \(180^\circ\). An RFC feeds collector DC while isolating the supply from RF. Each positive drive peak injects a current pulse containing fundamental and harmonics. The parallel tank presents high impedance at its resonant frequency,

\[ \boxed{f_0=\frac1{2\pi\sqrt{LC}}}, \]

so the fundamental develops a large voltage; off-resonant harmonics are suppressed. During cutoff, stored energy continues to exchange between \(L\) and \(C\) and feed the load. Pulses replace tank/load loss each cycle.

For a parallel loss \(R_p\),

\[ Q_p=\frac{R_p}{\omega_0L}=\omega_0CR_p. \]

For inductor series loss \(r_s\), \(Q_0\approx\omega_0L/r_s\). External loading reduces this to \(Q_L\), and

\[ \boxed{BW=f_2-f_1=\frac{f_0}{Q_L}}. \]

Output and DC powers are \(P_o=V_{o,rms}^2/R_L\) and \(P_{DC}=V_{CC}I_{DC}\), giving \(\eta=P_o/P_{DC}\). Class C is efficient because device voltage and current overlap briefly, although tank, device and matching losses lower practical efficiency.

Advantages are high selectivity, harmonic rejection and RF efficiency. Disadvantages are narrow bandwidth, detuning with component/load changes, alignment, inductor loss and component stress. Applications include RF transmitters, radio links, tuned receiver/IF stages, frequency multipliers and oscillators.

Practice target: 18 minutes; draw the RFC/tank path, trace pulse injection and free tank exchange, state resistance-specific \(Q\) formulas and finish with \(f_0\), \(BW\) and efficiency.

Model Answer — Role of the Parallel LC Tank [5 marks]¶

Model Answer — Class C and Linear Audio [5 marks]¶

Model Answer — Tuned Amplifier in Communications [5 marks]¶

Exam-ready answer

A tuned amplifier is an active amplifier whose collector or drain load contains a resonant network, usually a parallel LC tank. Its voltage gain is maximum around a selected center frequency \(f_0\) and falls on both sides, so the stage has a band-pass response. The resonant frequency and loaded bandwidth are

\[ f_0=\frac{1}{2\pi\sqrt{LC}}, \qquad BW=f_2-f_1=\frac{f_0}{Q_L}. \]

Its primary communications use is frequency or channel selection. In a radio or television receiver front end, varying \(L\) or \(C\) aligns \(f_0\) with the wanted carrier. The desired channel is then amplified strongly, while adjacent channels, noise and distant frequencies are attenuated. Tuned stages are also used at receiver RF and IF frequencies to obtain selectivity before demodulation.

In an RF transmitter, a tuned power stage provides the required carrier-frequency output, suppresses harmonic voltage and can incorporate impedance matching to the following network or antenna. Class-C operation is commonly used there for high efficiency. Thus the tuned amplifier combines active gain with narrowband filtering; it should not be confused with a passive filter, which provides selection but no power gain.

Practice target: 8 minutes; define the resonant load, draw a peaked response with \(f_0\), \(f_1\) and \(f_2\), then state one receiver and one transmitter use.

Model Answer — Frequency-Response Comparison [5 marks]¶