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Section D7: Amplifier Coupling& Multistage Analysis

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Section D7: Amplifier Coupling& Multistage Analysis So far, we‘ve talked about coupling in terms of using capacitors on the signal source and load in our single stage amplifier configurations. These capacitors (which we assumed were ideal) provided us with complete dc isolation for biasing purposes and acted as ideal shorts under ac conditions. In this section, we‘re going to focus on amplifiers that are composed of more than one stage. For these systems, it is necessary to connect, or couple, the individual stages to each other. Specifically, we will be looking at capacitive, direct, and transformer coupling between transistor stages, in addition to the input and output. Capacitive Coupling Capacitive coupling is exactly what we‘ve been doing so far. It is the simplest and most effective way to remove the effects of any dc levels between amplifier stages, since the capacitor removes the dc component from the ac signal. This is particularly important in multistage amplifiers because we want to be sure not to amplify any dc levels, which may drive our amplifier into saturation and render the output useless. Capacitive coupling allows us to treat each stage as an individual in terms of biasing. We will continue to assume that the capacitors used are large so we can say that they are essentially short circuits for the frequency range of interest. (Practically, this will never be the case and capacitors should be chosen such that the signal is not significantly changed, but we‘ll get into that later.) A two stage, capacitive coupled ER-CE amplifier is shown to the right. Note that there is a single dc source (VCC), as well as the signal ground, common to both stages. By convention, components have an identifying number or symbol to differentiate between stages. For example, the emitter resistor on stage one is denoted RE1, while the emitter resistor on stage two is RE2. This is an extremely good habit to get into! While it may seem like busy work for a two or even three- stage amplifier, when you get up in the tens, dozens, or hundreds, it is the only way to survive! Also, note that individual transistors are labeled by the symbol ”Q‘ and are numbered (symbols or letters may be used also) to correspond to a unique stage of the system. It doesn‘t matter if the transistor is an npn or pnp for labeling purposes, just make sure that every one has a unique label. Direct Coupling Direct coupling is just what it sounds like œ two amplifier stages are direct coupled if the output of the first stage is connected to the input of the second without the use of capacitors. A direct-coupled two-stage ER-ER amplifier is illustrated in Figure 5.14(a) of your text and is reproduced (slightly modified) to the right. As with the capacitive coupling scheme, components of individual stages are identified with a unique designator (a number in the figure above). However… note that there are different supply voltages for each stage in the figure above. This is a major difference between direct and capacitive coupling and comes from the fact that the dc voltage level of the first stage output interacts with the dc voltages of the second stage. If you analyze the figure above, you can see that essentially the first stage acts as the biasing circuitry for the second stage. Also, since there is no dc isolation from a capacitor, the ac output of the first stage is superimposed upon the dc quiescent level of the second stage. If we‘ve got more than two stages to the amplifier, this effect cascades throughout. To compensate for the bias level change, we have to use both positive and negative dc voltage sources as shown in the figure above. A level shifter (that we‘ll talk about next semester) provides the necessary bias voltage change. Another potential problem of direct coupling is the fact that it is sensitive to drift, or a slowly changing dc level. Pretty squirrelly, huh? You may be asking yourself, with all this hassle why are we even having this discussion? (Be honest now!) Well, it turns out that removing coupling capacitors, which are frequency sensitive elements (remember ZC=-j/ωC), from the circuit improves the low-frequency response of the amplifier and allows amplification of dc signals. Also, in terms of integrated circuits, the fewer components that have to be put on a chip (capacitors and bias resistors), the less real estate is required and overall fabrication process becomes simpler. A common use of the direct-coupled strategy is found in Figure 5.14(b) of your text and is reproduced to the right. In this figure, the first stage is an ER amplifier and the second stage is a CC (EF) amp. Recall from the previous section that this strategy allows us to use the ER amp as a gain stage and the CC (EF) as a buffer between the gain stage and the load. The CC (EF) stage has a gain of approximately unity (one) so it provides almost the same signal to the output as it accepts at the input. However, the CC (EF) stage reduces the very large output impedance of the ER stage to a much lower value that will allow effective connection to the load. In this configuration, the CC(EF) stage is seen as the load to Q1, while the ER stage provides the biasing for Q2. Example 5.7 of your text provides a good example of this two-stage amplifier, but I would like to present a caution. Your author states that VBB(Q2)=VCEQ(Q1). Although it turns out that RE1 is small, and this approximation is valid, the true expression should be VB (Q2) = VCEQ (Q1) + VE (Q1), where VB (Q2) = VE (Q2) + VBE (Q2) . In Figure 5.14(b), VE(Q1)=VRE1 and VE(Q2)=VRE2. The approach taken in Example 5.7 is legitimate œ make the assumption that VE is negligible, solve for appropriate parameters, then check your assumption to make sure it was valid. Transformer Coupling An npn transistor with a transformer at the emitter is shown to the right (Note: this figure is based on Figure 5.15 of your text). From circuit theory, recall the following characteristics and properties of an ideal transformer: N1 gives the number of turns in the primary coil and N2 is the number of turns in the secondary coil. The turns ratio may be expressed as N1:N2 as shown in the figure, a:1 (where a=N1/N2), or 1:a (where a=N2/N1). The input (primary side) and output (secondary side) voltages of the transformer are related through ≈ N ’ ∆ 2 v2 = v1 ∆ . « N1 If N2 > N1, v2 > v1 and the voltage is —stepped-up.“ Similarly, if N2 < N1, v2 < v1 and the voltage is —stepped-down.“ Since power must be conserved, the input and output currents are related inversely, or ≈ N ’ ∆ 1 ÷ i2 = i1 ∆ ÷ . « N 2 ◊ Finally, the relationship of the impedance seen at the primary side and the impedance at the secondary side (remember that if we‘re dealing with purely resistive circuits, all the Z‘s turn into R‘s) is ≈ ’ 2 ∆ N 2 ÷ Z 2 = Z1 ∆ ÷ . « N1 ◊ From the above expressions, we can see that transformers may be used for several functions in an amplifier circuit. By choosing an appropriate turns ratio, a transformer can be used to increase either the voltage or current gain, or to provide impedance matching with a load. Transformer coupling is often used for high frequency amplification, and may be used to form a bandpass filter. There is no free lunch, however. This type of coupling requires the tradeoff of additional cost œ whether monetary in terms of additional components, or in terms of real estate and fabrication complexity for integrated circuits. We won‘t be dealing with the specifics of biasing these circuits until next semester, but Example 5.8 illustrates the analysis of an ER amplifier that is transformer coupled on the input and output. Multistage Amplifier Analysis A generic multistage amplifier with three series stages is shown below in black box format (Figure 5.21 in your text). This series representation is a common form of amplifier system construction and is referred to as cascaded amplifier stages. The individual stages do not have to have the same voltage or current gain and are often different amplifier configurations (CE, ER, CC (EF), and CB), depending upon the system specifications to be satisfied. Each stage is analyzed independently, with the load on the first amplifier equal to the input resistance of the second stage, and the load on the second stage the input resistance of the third amplifier (this process continues for however many amplifier stages are cascaded). Since the beginning ends up being dependent on the end, we start at the output and proceed towards the input when designing or analyzing multistage amplifiers. It is easily proven, but we‘ll take it on faith, that the overall system gain is the product of the gain of the individual stages or, using the notation of your author: Av=Av1*Av2*Av3=ABC, and Ai=Ai1*Ai2*Ai3=XYZ. Using the gain impedance formula, the overall voltage and current gain are related by: R ABC = XYZ L . (Equation 5.52) Rin So, for multistage amplifiers, the tasks are the same, but the bookkeeping gets a little more interesting! The Cascode Configuration A common, and very useful, multistage amplifier is known as the cascode configuration, shown at the right (based on Figure 5.26(a) of your text).
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