Amplifier frequency response can be determined by splitting the circuit into two models, one valid at low frequencies where coupling and bypass capacitors are most important, and a second valid at high frequencies in which the internal device capacitances control the frequency-dependent behavior of the circuit.
Direct analysis of these circuits in the frequency domain, although usually possible for single-transistor amplifiers, becomes impractical for multistage amplifiers. In most cases, however, we are primarily interested in the midband gain and the upper- and lower-cutoff frequencies of the amplifier, and estimates of fH and fL can be obtained using the open-circuit and short-circuit time-constant methods. More accurate results can be obtained using SPICE circuit simulation.
The frequency-dependent characteristics of the bipolar transistor are modeled by adding the base-emitter and base-collector capacitors Cπ and Cμ and base resistance rx to the hybrid-pi model. The value of Cπ is proportional to collector current IC, whereas Cμ is weakly dependent on collector-base voltage. The rxCμ product is one important figure of merit for the frequency limitations of the bipolar transistor.
The frequency dependence of the FET is modeled by adding gate-source and gate-drain capacitances, CGS and CGD, to the pi-model of the FET. The values of CGS and CGD are independent of operating point when the FET is operating in the active region.
Both the BJT and FET have finite current gain at high frequencies, and the unity gain- bandwidth product ωT for both devices is determined by the device capacitances and the transconductance of the transistor. In the bipolar transistor, the β-cutoff frequency ωβ represents the frequency at which the current gain is 3 dB below its low-frequency value.
In SPICE, the basic high-frequency behavior of the bipolar transistor is modeled using these parameters: forward transit-time TF, zero-bias collector-base junction capacitance CJC, collector junction built-in potential VJC, collector junction grading factor MJC, and base resistance RB.
In SPICE, the high-frequency behavior of the MOSFET is modeled using the gate-source and gate-drain capacitances determined by the gate-source and gate-drain overlap capacitances CGSO and CGDO, as well as TOX, W, and L.
If all the poles and zeros of the transfer function can be found from the low- and high- frequency equivalent circuits, then fH and fL can be accurately estimated using Eqs. (17.16)and (17.23). In many cases, a dominant pole exists in the low- and/or high-frequency responses, and this pole controls fH or fL. Unfortunately, the complexity of most amplifiers precludes finding the exact locations of all the poles and zeros except through numerical means.
For design purposes, however, one needs to understand the relationship between the device and circuit parameters and fH and fL. The short-circuit time constant (SCTC) and open-circuit time constant (OCTC) approaches provide the needed information and were used to find detailed expressions for fH and fL for the three classes of single-stage amplifiers,the inverting, noninverting, and follower stages.
It was found that the inverting amplifiers provide high gain but the most limited bandwidth. Noninverting amplifiers can provide improved bandwidth for a given voltage gain, but it is important to remember that these stages have a much lower input resistance. The follower configurations provide unity gain over a wide bandwidth. The three basic classes of amplifiers show the direct trade-offs that occur between voltage gain and bandwidth.
The OCTC and SCTC methods can also be used to determine the upper- and lower- cutoff frequencies of multistage amplifiers. The frequency responses of the differential pair, cascode amplifier, C-C/C-B cascade stage, and current mirror were all evaluated, as well as an example of calculations for a three-stage amplifier.
The input impedance of an amplifier is decreased as a result of Miller multiplication, and the expression for the dominant pole of an inverting amplifier can be cast in terms of the Miller effect. Miller multiplication represents a useful method for setting the unity-gain frequency of internally compensated operational amplifiers. This technique is often called Miller compensation. In these op amps, slew rate is directly related to the unity-gain frequency.
Tuned amplifiers employing RLC circuits can be used to achieve narrow-band amplifiers at radio frequencies. Designs can use either single- or multiple-tuned circuits. If the circuit sin a multiple-tuned amplifier are all designed to have the same center frequency, the circuit is referred to as synchronously tuned. If the tuned circuits are adjusted to different center frequencies, the circuit is referred to as stagger-tuned. Care must be taken to ensure that tuned amplifiers do not become oscillators, and the use of the cascode and C-C/C-B cascade configurations offer improved isolation between multiple-tuned circuits.
Mixer circuits are widely used in communications electronics to translate the frequency spectrum of a signal. Mixing requires some form of multiplication of two signals, which generates sums and differences of the two input spectra. Single- and double-balanced configurations eliminate one or both of the input signals from the output spectrum. Single-balanced mixers can be designed using differential pairs. Double-balanced mixers often utilize circuits based on the Gilbert multiplier.
Single- and double-balanced modulator circuits are closely related to mixers, and the Gilbert multiplier can be used to generate double-side band surpressed-carrier (DSBSC) signals as well as amplitude-modulated waveforms.
