# 3.1: Introduction


Wideband amplifier design requires the synthesis of matching networks that provide a match over considerable bandwidths. The divisions between narrowband, wideband and ultra-wideband microwave amplifier design depend on operating frequency and the amplifier efficiency required. Generally, however, a microwave amplifier with a half-octave bandwidth, e.g. $$2$$ to $$3\text{ GHz}$$, is regarded as a wideband design.

The essential amplifier design problem is that at microwave frequencies the parasitic input and output capacitances of a transistor are significant and these must be canceled to achieve maximum power transfer. Synthesis of the input and output matching networks of a microwave amplifier at a single frequency leads to a narrowband amplifier with a bandwidth of perhaps $$2–3\%$$. At lower frequencies where the parasitic capacitances are less significant, the fractional bandwidth may be greater. An ideal response would be achieved if there were negative capacitors and typically resonance of lumped-elements can be used to at least partially present a negative capacitance-like characteristic over about a quarter-octave bandwidth.

The dominant reactive parasitics of a transistor are its input and output capacitances, but also the feedback capacitor between the collector/drain and base/gate becomes important at higher frequencies. Ignoring the feedback capacitance and thinking just about the input of the transistor, the input of the transistor is a capacitance sometimes in series (for a BJT) and sometimes in parallel (for a FET) with the resistance describing the absorption of RF input power by the transistor. Ideal matching requires the synthesis of a negative capacitor (i.e., an element which has an inductive reactance that reduces with frequency). Simply using an inductor to provide matching provides a matching element whose impedance increases with frequency. The wideband input matching problem becomes essentially the synthesis of a terminated two-port network with an input impedance that has the required negative capacitance characteristic. This is not easy to achieve using lumped-elements alone.

This chapter presents three strategies for designing wideband linear amplifiers. One uses the image impedance method in which the required negative capacitance impedance is realized using a transmission line network. The next is a multistage distributed amplifier that incorporates the transistor capacitances into a transmission line. The third approach is akin to a parallel coupled-line filter design.

## 3.1.1 Wideband Amplifier Design Strategies

Generally a wideband amplifier has a half-octave bandwidth, e.g. $$8\text{ GHz}$$ to $$12\text{ GHz}$$. Multiple objectives must be met in wideband amplifier design. Of course the gain must be flat over the specified bandwidth but it is also important to meet noise and stability objectives over the bandwidth. Of course the amplifier must be stable out-of-band as well. It is generally not possible to meet all of these objectives using computer optimization and it is necessary to simplify the design process. When computer optimization is used, it is done in stages and begins with a prototype design that is not too far away from the final design.

An ultra-wideband amplifier has a bandwidth of more than a half octave. There are two approaches to achieving ultra-wide bandwidth and both types of amplifiers have low efficiency. The first category of ultra-wideband amplifier is the distributed amplifiers which achieves multi-octave bandwidth by incorporating the parasitic capacitances of transistors in an artificial transmission line. The parasitic inductances are usually negligible but if not, they are incorporated in the artificial transmission line. In effect there is a multi-stage amplifier and each stage must be a Class A stage and thus have very low efficiency, think $$5\%$$. Ultra-wideband distributed amplifiers tend to be used in instrumentation. A non-aggressive Class A amplifier design is more likely to be stable. Distributed amplifier design is considered in Section 3.2 and a case study of a distributed amplifier in Section 3.3.

A second type of ultra-wideband amplifier is an operational amplifier with very high levels of feedback. In an operational amplifier the open loop amplifier (without feedback) has very high gain, but a gain that varies significantly with frequency. Then feedback is used, the loop is closed, to effectively throw away most of the gain to obtain an overall flatter gain over a wide bandwidth. This type of amplifier has very low efficiency and usually the gains available from microwave transistors are not high enough anyway. Even with the highest performing transistors, that is ones with very high $$S_{21}$$ to $$S_{12}$$ ratio, the transistors tend to be very expensive requiring finer lithography to achieve the required shorter gate. Microwave operational amplifiers really are not viable and so will not be considered further.

The highest bandwidth of a microwave amplifier that achieves flat gain across the band, has good efficiency, and meets noise and stability requirements is about half an octave. A straight-forward approach would seem to be to simultaneously design the input and output networks and employ computer optimization. This is complicated at microwave frequencies because feedback from the output to the input, i.e. $$S_{12}$$, is large. Design then becomes an optimization problem with multiple objectives and many parameters to adjust. An optimization-only approach rarely works. It is essential to simplify the problem and approach design in stages. The most successful wideband amplifier design technique is the negative image design method which begins by placing hypothetical negative capacitors in parallel with the input and output capacitances of a transistor. The procedure will be described in Section 3.4 and then a case study is presented in Section 3.5.

A final class of microwave amplifiers that achieves reasonably high bandwidths are the differential amplifiers used in RFICs. These are considered in Sections 3.6–3.8.

3.1: Introduction is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.