DEFINITIONS AND BASIC CONCEPTS
The frequency response of an electronic device or system is the variation it causes. if any. in the level of its output signal when the frequency of the signal is changed. In other words. it is the manner in which the device responds to changes in signal frequency. Variation in the level (amplitude. or rms value) of the output signal is
usually accompanied by a variation in the phase {of the output relative to the input. so the term frequency response also refers to phase shift as a function of frequency. (Phase shift versus frequency is sometimes called phase response.i Figure 10-1 shows an amplifier whose frequency response causes small output amplitudes
at both low and high frequencies. Notice that the input signal amplitude is the same at each frequency, but the output signal amplitude changes with frequency. Thus, the gain of the amplifier is a function of frequency. In this example the gain is small at the low frequency and small at the high frequency. The frequency response of an amplifier is usually presented in the form of a graph that shows output amplitude (or, more often, voltage gain) plotted versus
frequency. Phase-angle variation is sometimes plotted on the same graph. Figure 10-2 shows a typical plot of the voltage gain of an ac amplifier versus frequency. Notice that the gain is 0 at (zero frequency), then rises as frequency increases, levels off for further increases in frequency, and then begins to drop again at high frequencies. The frequency range over which the gain is more or less constant (“flat”) is called the range, and the gain ‘in that range is designated Am. As shown in Figure 10-2, the low frequency at which the gain equals ( 2) Au is called the lower ell/off frequency and is designated fl’ The high frequency at which the gain once again drops to O. is called the cutoff frequency and is designated h- The bandwidth of the amplifier is defined to be the difference between the upper and lower cutoff frequencies:
The points on the graph in Figure 10-2 where the gain is O.707A,. are often called half-power points, and the cutoff frequencies are sometimes called half-power frequencies, because the output power of the amplifier at cutoff is one-half of its output power in the range. To demonstrate this fact, suppose that an output voltage v is developed across R ohms in the range. Then the output power in midband is An audio amplifier has a lower cutoff frequency of 20 Hz and an upper cutoff frequency of 20 kHz. (This is the frequency range of sound waves-the audio frequency range.) The amplifier delivers 20 W to a 12-12 load at 1 kHz.
1. What is the bandwidth of the amplifier?
2. What is the rms load voltage a 20 kHz?
3. What is the rms land voltage at 2 kHz?
Solution
1. BW = f2 – f, = 20 X 103 Hz – 20 Hz = 19,980 Hz
2. Since 1 kHz is in the midband range, the midband power is 20 W. At the 20-kHz cutoff frequency, the power is Y2(20) = 10 W, so 3. Assuming that the load voltage is exactly the same throughout the midband range (not always the case in practice), the output at 2 kHz will be the same as that at 1 kHz, and we can use equation 10-2 with P = 20 W to solve for v. Alternatively, the midband voltage equals the voltage at cutoff divided by 0.707:
Amplitude and Phase Distortion
The signal passed through an ac amplifier is usually a complex waveform containing many different frequency components rather than a single-frequency (“pure”) sine wave. For example, audio-frequency signals such as speech and music are combinations of many different sine waves occurring simultaneously with different amplitudes and different frequencies, in the range from 20 Hz to 20 kHz. As another example, any periodic waveform. such as a square wave or a triangular wave, can be shown to be the sum of a large number of sine waves whose amplitudes and frequencies can be determined mathematically. In previous discussions, we have analyzed ac amplifiers driven by single-frequency, sine-wave sources. This approach is justified by the fact that signals of all kinds can be regarded as sums of sine waves, as just described, so it is enough to know how an amplifier treats any single sine wave to know how it treats sums of sine waves (by the superposition principle). In order for an output waveform to be an amplified version of the input, an amplifier must amplify every frequency component III the signal by tile same amount. For example, if an input signal is the sum of a O.S-V 100-Hz sine wave, a 0.2-V-rms, I-kl-lz sine wave, and a O.7-V-rms, 10-kHz sine wave, then an amplifier having gain 10 must amplify each frequency component by 10, so that the output consists of a 5- v-rrns. lOO-Hz sine wave, a 2·V-rms. 1-kHz sine wave.zand a 7-V-rms, 10-kHz sine wave. If the frequency response of an amplifier is such that the gain.
