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Chapter 17 “Transforms” Rin to the Value Rgen (As Seen by the Generator) and at the Same Time Nullifies the Reactance

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Chapter 17 “Transforms” Rin to the Value Rgen (As Seen by the Generator) and at the Same Time Nullifies the Reactance Receivers, Transmitters, Transceivers and Projects 17 this chapter, William E. Sabin, W0IYH, discusses the “system design” of Amateur Radio receivers, transmitters and transceivers. “A Single-Stage Building Block” reviews briefly a In few of the basic properties of the various individual building block circuits, described in detail in other chapters, and the methods that are used to combine and interconnect them in order to meet the requirements of the completed equipment. “The Amateur Radio Communication Channel” describes the relationships between the equipment system design and the electromagnetic medium that conveys radio signals from transmitter to receiver. This understanding helps to put the radio equipment mission and design requirements into perspective. Then we discuss receiver, transmitter, transceiver and transverter design techniques in general terms. At the end of the theory discussion is a list of references for further study on the various topics. The projects section contains several hardware descriptions that are suitable for amateur construction and use on the ham bands. They have been selected to illustrate system-design methods. The emphasis in this chapter is on analog design. Those functions that can be implemented using digital signal processing (DSP) can be explored in other chapters, but an initial basic appreciation of analog methods and general system design is very valuable. A SINGLE-STAGE BUILDING BLOCK We start at the very beginning with Fig 17.1, a generic single-stage module that would typically be part of a system of many stages. A signal source having an “open-circuit” voltage Vgen causes a current Igen to flow through Zgen, the impedance of the generator, and Zin, the input impedance of the stage. This input current is responsible for an open-circuit output voltage Vd (measured with a high-impedance voltmeter) that is proportional to Igen. Vd produces a current Iout and a voltage drop across Zout, the output impedance of the stage and Zload, the load impedance of the stage. Observe that the various Zs may contain reactance and resistance in various combinations. Let’s first look at the different types of gain and power relationships that can be used to describe this stage. Actual Power Gain 2 Current Igen produces a power dissipation Pin in the resistive component of Zin that is equal to Igen Rin. The current Iout produces a power dissipation Pload in the resistive component of Zload that is equal 2 to Iout Rload. The actual power gain in dB is 10 log (Pload / Pin). This is the conventional usage of dB, to describe a power ratio. Receivers, Transmitters, Transceivers and Projects 17.1 Fig 17.1—A single-stage building-block signal processor. The properties of this stage are discussed in the text. Voltage Gain The current Igen produces a voltage drop across Zin. Vd produces a current Iout and a voltage drop Vout across Zload. The voltage gain is the ratio Vout / Vin (1) In decibels (dB) it is 20 log (Vout / Vin) (2) This alternate usage of dB, to describe a voltage ratio, is common practice. It is different from the power gain mentioned in the previous section because it does not take into account the power ratio or the resistance values involved. It is a voltage ratio only. It is used in troubleshooting and other instances where a rough indication of operation is needed, but precise measurement is unimportant. Voltage gain is often used in high-impedance circuits such as pentode vacuum tubes and is also sometimes convenient in solid-state circuits. Its improper usage often creates errors in radio circuit design because many calculations, for correct answers, require power ratios rather than voltage ratios. We will see several examples of this throughout this chapter. Available Power 2 The maximum power, in watts, that can be obtained from the generator is Vgen / (4 Rgen). To see this, suppose temporarily that Xgen and Xin are both zero. Then let Rin increase from zero to some large value. The maximum power in Rin occurs when Rin = Rgen and the power in Rin then has the value mentioned above (plot a graph of power in Rin vs Rin to verify this, letting Vgen = 1 V and Rgen = 50 W). This is called the “available power” (we’re assuming sine-wave signals). If X gen is an inductive (or capacitive) reactance and if Xin is an equal value of capacitive (or inductive) reactance, the net series reactance is nullified and the above discussion holds true. If the net reactance is not zero the current Igen is reduced and the power in Rin is less than maximum. The process of tuning out the reactance and then transforming the resistance of Rin is called “conjugate matching.” A common method for doing this conjugate matching is to put an impedance transforming circuit of some kind, such as a transformer or a tuned circuit, between the generator and the stage input that 17.2 Chapter 17 “transforms” Rin to the value Rgen (as seen by the generator) and at the same time nullifies the reactance. Fig 17.2 illustrates this idea and later discussion gives more details about these interstage networks. A small amount of power is lost within any lossy elements of the matching net- work. This same technique can be used between the output of Fig 17.2—The conjugate impedance match of a generator to a stage the stage in Fig 17.1 and the input. The network input impedance is Rgen m jXgen and its output load impedance Zload. In this impedance is Rin m jXin (where either R term may represent a dy- case, the stage delivers the namic impedance). Therefore the generator and the stage input are both impedance matched for maximum power transfer. maximum amount of power to the load resistance. If both in- put and output are processed in this way, the stage utilizes the generator signal to the maximum extent possible. It is very important to note, however, that in many situations we do not want this maximum utilization. We deliberately “mismatch” in order to achieve certain goals that will be discussed later (Ref 1). The dBm Unit of Power In low-level radio circuitry, the watt (W) is inconveniently large. Instead, the milliwatt (mW) is commonly used as a reference level of power. The dB with respect to 1 mW is defined as dBm = 10 log (PW / 0.001) (3) where dBm = Power level in dB with respect to 1 mW PW = Power level, watts. For example, 1 W is equivalent to 30 dBm. Also m/10 PW = 0.001 × 10 dB (4) Maximum Available Power Gain 2 The ratio of the power that is available from the stage, Vd / (4 Rout), to the power that is available 2 from the generator, Vgen / (4 Rgen), is called the maximum available power gain. In some cases the circuit is adjusted to achieve this value, using the conjugate-match method described above. In many cases, as mentioned before, less than maximum gain is acceptable, perhaps more desirable. Available Power Gain Consider that in Fig 17.1 the stage and its output load Zload constitute an “expanded” stage as defined by the dotted box. The power available from this new stage is determined by Vout and by Rstage, the 2 2 resistive part of Zstage. The available power gain is then Vout / (4 Rstage) divided by Vgen / (4 Rgen). This value of gain is used in a number of design procedures. Note that Zload can be a physical network of some kind, or it may be partly or entirely the input impedance of the stage following the one shown in Fig 17.1. In the latter case it is sometimes convenient to “detach” this input impedance from the next stage and Receivers, Transmitters, Transceivers and Projects 17.3 make it part of the expanded first stage, as shown in Fig 17.1, but we note that Zout is still the generator (source) impedance that the input of the next stage “sees.” Transducer Power Gain The transducer gain is defined as the ratio of the power actually delivered to Rload in Fig 17.1 to the power that is available from the generator Vgen and Rgen. In other words, how much more power does the stage deliver to the load than the generator could deliver if the generator were impedance matched to the load? We will discuss how to use this kind of gain later. Feedback (Undesired) One of the most important properties of the single-stage building block in Fig 17.1 is that changes in the load impedance Zload cause changes in the input impedance Zin. Changes in Zgen also affect Zout. These effects are due to reverse coupling, within the stage, from output to input. For many kinds of circuits (such as networks, filters, attenuators, transformers and so on) these effects cause no unexpected problems. But, as the chapter on RF Power Amplifiers explains in detail, in active circuits such as amplifiers this reverse coupling within one stage can have a major impact not only on that stage but also on other stages that follow and precede. It is the effect on system performance that we discuss here. In particular, if a stage is expected to have certain gain, noise factor and distortion specifications, all of these can be changed either by reverse coupling (undesired feedback) within the stage or adjacent stages. For ex- ample, internal feedback can cause the input impedance of a certain stage “A” (Fig 17.1) to become very large. If this impedance is the load impedance for the preceding stage, the gain of the preceding stage can become excessive, creating problems in both stages.
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