
IntroductionThe topic of this tutorial is amplifiers. Although the topic may seem mundane on first glance, it is actually key to almost all of analog electronics. Without amplifier circuits most of electronics simply would not work. We will start out by looking at the most basic problem of electronics: overcoming the effects of noise. The purpose of the amplifier is to build up the signal without adding too much to the noise so that a superior signaltonoise ratio exists. We will look at transistor amplifiers including bipolar NPN/PNP transistors, junction fieldeffect transistors and MOSFET transistors. We will look at the ubiquitous operational amplifier (“opamp” or “opamp”), as well as both audio smallsignal and power amplifiers. Radio frequencies are not neglected. Sections are included on smallsignal RF Amplifiers, solidstate parametric amplifiers, and Monolithic Microwave Integrated Circuits (MMICs). The latter circuits operate from near DC to well over 1,000 MHz and have an inherent 50ohm input and output impedance. We will also explore the practical end of amplifier technology. Finally, we will cover two popular topics: troubleshooting solidstate amplifier circuits and selecting solidstate replacement parts. Signals and NoiseThe amplification of signals is basically an issue of fighting any noise that is in the circuit. Figure 11A shows a noise level with three different signals. SignalA would be totally obscured by the noise produced by the signal and/or received from the input source. The other two signals (B and C) are progressively better able to be used. The issue is that the signaltonoise ratio (SNR) improves in each case. The higher the SNR, the better the detection of the signal. Figure 11A. Signals must be above the noise to be usable: SignalA below the noise, signalB marginally above the noise, signalC significantly above the noise. Although gain, bandwidth and the shape of the passband are important amplifier characteristics, we must concern ourselves about circuit noise. In the spectrum below, VHF manmade and natural atmospheric noise sources are so dominant that receiver noise contribution is trivial, but at VHF and above, receiver and amplifier noise sets the performance of the system. At any temperature above absolute zero (0°K or 273°C) electrons in a material are in constant random motion. Because of the inherent randomness of that motion, however, there is no detectable current in any direction. In other words, electron drift in any single direction is cancelled over short times by equal drift in the opposite direction. There is, however, a continuous series of random current pulses generated in the material, and those pulses are seen by the outside world as a noise signal. This signal is called by several names: thermal agitation noise, thermal noise or Johnson noise. It is important to understand what we mean by “noise” in this context. In a communications or instrumentation system the designer may regard all unwanted signals as “noise,” including manmade electrical spark signals and adjacent channel communications signals as well as Johnson noise. In other cases, the harmonic content generated in a linear signal by a nonlinear network could be regarded as “noise,” but in the context of amplifiers and of radio receivers, “noise” refers to thermal agitation (Johnson) noise. Amplifiers and other linear networks are frequently evaluated using the same methods even though the two classes appear radically different. In the generic sense, a passive network is merely an amplifier with negative gain or a complex transfer function. We will consider only amplifiers here but keep in mind that the material herein also applies to other forms of linear (passive) network. Amplifiers are evaluated on the basis of signaltonoise ratio (SIN or SNR). The goal of the designer is to enhance the SNR as much as possible. Ultimately, the minimum signal detectable at the output of an amplifier is that which appears above the noise level; therefore, the lower the system noise, the smaller the mini mum detectable signal (MDS). Noise resulting from thermal agitation of electrons is measured in terms of noise power (P_{n}) and carries the units of power (watts or its subunits). Noise power is found from: P_{n} = KTB eq.(11) Where: P_{n} is the noise power in watts (W) K is Boltzmann’s constant (1.38 x 10^{23} J/(K) B is the bandwidth in hertz (Hz) Notice in Equation (11) that there is no center frequency term, only a bandwidth. True thermal noise is gaussian or neargaussian in nature so frequency content, phase and amplitudes are equally distributed across the entire spectrum; this is called “equipartition distribution” of energy. Thus, in bandwidth limited systems, such as a practical amplifier or network, the total noise power is related only to temperature and bandwidth. We can conclude that a 20 MHz bandwidth centered on 1 GHz produces the same thermal noise level as a 20 MHz bandwidth centered on 4 GHz or some other frequency. Noise sources can be categorized as either internal or external. The internal noise sources are due to thermal currents in the semiconductor material resistances. It is the noise component contributed by the amplifier under consideration. If noise or S/N ratio is measured at both input and output of an amplifier, the output noise is greater. The internal noise of the device is the difference between output noise level and input noise level. External noise is the noise produced by the signal source, so it is often called source noise. This noise signal is due to thermal agitation currents in the signal source, and even a simple zerosignal input termination resistance has some amount of thermal agitation noise. Both types of noise generator are shown schematically in Figure 11B. Here we model a microwave amplifier as an ideal “noiseless” amplifier with a gain of G and a noise generator at the input. This noise generator produces a noise power signal at the input of the ideal amplifier. Although noise is generated throughout the amplifier device, it is common practice to model all noise generators as a single inputreferred source. This source is shown as voltage V_{i} and current l_{i} Figure 11B. Equivalent circuit of an amplifier. NOISE FACTOR, NOISE FIGURE AND NOISE TEMPERATUREThe noise of a system or network can be defined in three different but related ways: noise factor (F_{n}), noise figure (NF) and noise temperature (T_{e}) NOISE FACTOR (F_{N}) The noise factor is the ratio of output noise power (Pno) to input noise power (P_{ni}): F_{N} = (P_{NO} / P_{NI)}  T=290K eq. (12) To make comparisons easier, the noise factor is always measured at the standard temperature (T_{o}) 290°K (approximately “room temperature”). The input noise power P_{ni} can be defined as the product of the source noise at standard temperature (T_{o}) and the amplifier gain: P_{NI} = GKBT_{o} eq.(13) It is also possible to define noise factor Fn in terms of output and input S/N ratio: F_{N} = SNR_{IN} / SNR_{OUT} eq. (14) which is also: F_{N} = (P_{NO} / (KT_{o}BG)) eq.(15) Where: SNR_{n} is the input signal to noise ratio SNR_{out} is the output signal to noise ratio P_{no} is the output noise power in watts (W) K is Boltzmann’s constant (1.38 x 10^{23} J/°K) T_{o} is 290 degrees Kelvin (°K) B is the network bandwidth in hertz (Hz) G is the amplifier gain (linear, not dB) The noise factor can be evaluated in a model that considers the amplifier ideal, and, therefore, only amplifies through gain G the noise produced by the “input” noise source: F_{N} = KT_{o}BG+ΔN / KToBG eq. (16A) F_{N} = ΔN / KT_{o}BG eq. (16B) Where: ΔN is the noise added by the network or amplifier All other terms are as defined above NOISE FIGURE (NF) The noise figure is a frequently used measure of an amplifier’s “goodness,” or its departure from “idealness.” Thus, it is a figure of merit. The noise figure is the noise factor converted to decibel notation: NF = 10 LOG F_{n} eq. (17) Where: NF is the noise figure in decibels (dB) F_{n} is the noise factor LOG refers to the system of base10 logarithms NOISE TEMPERATURE (T_{e}) The noise “temperature” is a means for specifying noise in terms of an equivalent temperature. Evaluating Equation (11) shows that the noise power is directly proportional to temperature in degrees Kelvin, and also that noise power collapses to zero at the temperature of Absolute Zero (0 °K). Note that the equivalent noise temperature T_{e} is not the physical temperature of the amplifier but rather a theoretical construct that is an equivalent temperature that produces that amount of noise power. The noise temperature is related to the noise factor by: T_{e} = (F_{N}  1)T_{o} eq.(18) and to noise figure by: T_{e} = KT_{o} [ANTILOG[ NF/10]] eq. (19) Now that we have noise temperature Te we can also define noise factor and noise figure in terms of noise temperature: F_{n} = [T_{e}/T_{o}] + 1 eq. (110) and, NF = 10Log [ [T_{e}/T_{o}] + 1] eq. (111) The total noise in any amplifier or network is the sum of internally generated and externally generated noise. In terms of noise temperature: P_{N(TOTAL)} = GKB(T_{o}+T_{e}) eq. (112) Where: P_{N(TOTAL)} is the total noise power (All other terms are as previously defined) Figure 12 shows the relationship between the noise figure in decibels and the noise temperature in Kelvins. NOISE IN CASCADE AMPLIFIERSA noise signal is seen by a following amplifier as a valid input signal. Thus, in a cascade amplifier the final stage sees an input signal that consists of the original signal and noise amplified by each successive stage. Each stage in the cascade chain both amplifies signals and noise from previous stages and also contributes some noise of its own. The overall noise factor for a cascade amplifier can be calculated from Friis’ noise equation: F_{n} = F_{1} + [(F_{2}1)/ G1] + [(F_{3}1)/ G1G2] + [(F_{n1})/ G1G2…G_{n1}] eq. (113) Where: F_{n} is the overall noise factor of N stages in cascade F_{1} is the noise factor of stage1 F_{2 }is the noise factor of stage2 F_{n} is the noise factor of the nth stage G_{1} is the gain of stage1 G_{2} is the gain of stage2 G_{n1} is the gain of stage (n1) Figure 12. Noise figure vs. noise temperature of amplifier. As you can see from Equation (113), the noise factor of the entire cascade chain is dominated by the noise contribution of the first stage or two. Typically, high gain amplifiers use a low noise device for only the first stage or two in the cascade chain. A threestage amplifier (Figure 13) has the following gains: G1=10, G2=10 and G3=25. The stages also have the following noise factors: F1 =1.4, F2=2 and F3= 36. Calculate a) the overall gain of the cascade chain in decibels, b) the overall noise factor, and c) the overall noise figure. Figure 13. Three amplifiers in cascade. Solution: (a) G=G1xG2xG3 G = (10) x (10) x (25) G=2500 G_{dB} = 10 LOG(2500) G_{dB} = (10)(3.4) = 34dB c) NF=10LOGF_{n} NF = (10)(LOG(1.53)) NF = (10)(0.19) = 1.9 dB Note in the above example that the overall noise factor (1.53) is only slightly worse than the noise factor of the input amplifier (1.4) and is better than the noise factors of the following stages (2 and 3.6, respectively). Clearly, the overall noise factor is set by the input stage. 
