6. Tuned Amplifiers // Electronic Circuit Analysis // bhaswanth

Where power amplifiers move energy, tuned amplifiers move narrow bands of frequency. The collector load is replaced with a parallel LC tank, sharply selective for one frequency.

6.1 Q factor and bandwidth

The Q factor of the resonant tank determines the bandwidth:

$BW = \frac{f_0}{Q}$

High Q gives narrow band (very selective). Low Q gives wider band (less selective). For a parallel LC tank with shunt resistance $R$ and resonant frequency $\omega_0 = 1/\sqrt{LC}$ :

$Q = R / (\omega_0 L) = R \omega_0 C$

To maximize Q, minimize losses: high-quality components (low-loss capacitors, low-resistance copper inductors), careful PCB design, and (for very narrow BW) crystal filters or surface-acoustic-wave (SAW) filters that achieve $Q$ in the thousands.

There is a fundamental tradeoff: high-Q tanks are very selective but ring for a long time (their impulse response is a slowly-decaying sinusoid). Low-Q tanks pass more bandwidth but have less selectivity. You cannot have both simultaneously, and this is the same uncertainty principle that limited time-frequency localization in Chapter 3.

6.2 Single-tuned amplifier

One LC tank. The frequency response is a single resonant peak centered at $f_0$ with bandwidth $f_0/Q$ . Used in IF strips of older AM radios. The classic 455 kHz IF amp in a transistor radio is a chain of single-tuned stages, each with a small adjustable inductor (the "IF can") that the technician peaks at the alignment frequency.

6.3 Double-tuned amplifier

Two coupled tanks. As the coupling between them increases, the response transitions from a single peak (when overcoupled, the tanks merge into a flat-topped response, the maximally-flat or Butterworth condition) to a wider, flatter response with two slight peaks (when undercoupled or critically coupled).

The Butterworth response is desirable: wider bandwidth than single-tuned, flat passband, sharper rolloff. Used heavily in IF strips of higher-quality radios and in classical amateur-radio receivers.

6.4 Stagger-tuning

Cascade synchronously-tuned stages (all at the same $f_0$ ) and the bandwidth narrows quickly with stage count, the same compounding we saw in section 2.3. Stagger-tuning slightly detunes each stage so the combined response is wider and flatter:

$f_n = f_0 + \delta_n$

with the offsets $\delta_n$ chosen so the cascade approximates a Butterworth or Chebyshev passband. Used in IF amplifiers of high-end radio receivers and military communications gear. Modern radios often replace this analog craftsmanship with digital filtering after an early ADC, but the math of stagger-tuning is exactly the analog forerunner of digital FIR filter design.

6.5 Stability of tuned amps and neutralization

A tuned amplifier with high gain at one frequency is exposed to a particular hazard: $C_\mu$ provides a feedback path from collector to base, and if the feedback at the resonant frequency has the wrong phase, the amplifier oscillates. (This is called regenerative feedback and was deliberately exploited by Edwin Armstrong in his regenerative receivers, but in a design where you want amplification rather than oscillation, it is a bug.)

Three remedies:

Neutralization. Add a deliberate feedback path (a small cap from a "180°-flipped" collector signal back to the base) that exactly cancels the Miller-cap contribution. Old vacuum-tube TV amplifier designs used neutralization extensively, with adjustable trimmers labeled "neutrodyne."
Cascode. Kills Miller in the input stage (we have seen this). The collector of the input transistor barely swings, so $C_\mu$ 's feedback path carries almost no signal.
Unilateralization. Even more aggressive than neutralization: eliminate not just the Miller component but the entire reverse path, including the part that comes from the package and PCB layout. Used in critical RF designs where unconditional stability is required.

6.6 Wideband amplifiers

The opposite of tuned: flat response from DC (or low frequency) to GHz. Achieved by:

Resistive collector loads instead of LC tanks (no resonance, no peak, but no high-impedance tank either, so gain is lower).
Heavy negative feedback (gives flat response by trading away gain).
Distributed amplifiers, in which the signal travels along a transmission line gathering gain from many transistors tapped along the line. Used in oscilloscope front-ends, network analyzers, and RF lab equipment up to tens of GHz.