One goal of cascading amplifier stages is to achieve higher levels of gain without sacrificing gain flatness across the design bandwidth of interest.
Amplifiers are designed for adding signal gain or achieving a target output-power level. As was demonstrated last month, it is possible to design a simple broadband amplifier for relatively flat gain performance from 50 to 1050 MHz. But if higher gain levels are required, it becomes necessary to cascade two or more amplifier stages, and the design becomes more complex. The final installment of this eight-part article series on transistor design addresses the steps that should be taken to ensure that cascaded stages provide a desired final gain level without sacrificing gain flatness.
Last month's broadband amplifier (Fig. 1) provided 15-dB gain within 0.5-dB from 50 to 1050 MHz using the HP 415868 transistor. Due to the good match, higher gain can be obtained by cascading two such amplifier stages, and the individual stage gains will add with very little mismatch error.1 This results in a gain for the two stages of 30 dB with about 1 dB flatness from 50 to 1100 MHz (Fig. 2).
This extension of broadband performance does not always follow when cascading. Here it occurs because the S11 and S22 magnitudes (Fig. 1) of each amplifier section are fairly small, especially S11. When either the input or output of a single-stage amplifier is well matched, the cascade combination of two of them will have relatively low mismatch interaction. The feedback method of broad banding employed last month in Part 7 yields a better match because it adjusts gain without introducing high reflection.
To illustrate this principle, suppose that the same set of goals were used to optimize the amplifier shown in Fig. 3. Its single-stage performance after optimization is also shown in Fig. 3. This circuit offers nearly the same gain flatness over the 50-to-1050-MHz bandwidth and also is unconditionally stable from DC to 6000 MHz. However, the input and output mismatches, S11 and S22, of this circuit are greater than those of the feedback-optimized circuit of Fig. 1. Consequently, when two of them are cascaded, as shown in Fig. 4, a larger variation of gain, almost ±3 dB over the 50-to-1050-MHz band, occurs due to the reflection interaction between them. This interaction is termed mismatch error.1
Designing broadband amplifiers and cascaded amplifier stages does require guesswork, euphemistically called optimization when performed with a computer. Certain strategies are useful in this pursuit. First, since transistor gain diminishes as frequency increases, circuitry that favors the passage of higher frequencies (series capacitors and shunt inductors) is more conducive to uniform gain. However, circuits which flatten gain by means of feedback may do so while providing lower S11 and S22 values, minimizing the mismatch error when the circuits are cascaded or used with other reflective components, such as reactive filters. Accordingly, when optimizing, S11 and S22 should be made part of the goals. At frequencies for which either S11 or S22 has a small value, two such circuits cascaded will have a low mismatch error at those frequencies.
In summary, for most amplifier designs the choices amount to what input and output impedance environments will be presented to the transistor over all of the frequency range for which it has gain. One must balance the need for gain against the requirements for unconditional stability, which is very important. An amplifier that breaks into oscillation is not just useless, it is a liability.
Often, design choices lead to amplifier networks that do not present a good match to either the input or output transmission lines. If the remainder of the system also has high mismatches as would be true, for example, if reactive filters are connected to the amplifier, the system performance will not be predictable unless those networks are modeled in conjunction with the amplifier.
Many points have been covered in this eight-part series on transistor amplifier design. In the end, engineering discretion is required to balance all of the desired amplifier attributes with the relatively few degrees of design freedom available. This is the artistry of design.
- Joseph F. White; High Frequency Techniques, An Introduction to RF and Microwave Engineering; John Wiley & Sons, Inc., Hoboken, NJ, 2004.