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The sinusoidal frequency response (or, simply, frequency response) of a circuit provides a measure of how the circuit responds to sinusoidal inputs of arbitrary frequency In other words, given the input signal amplitude, phase, and frequency, knowledge of the frequency response of a circuit permits the computation of the output signal The box Fourier Analysis provides further explanation of the importance of sinusoidal signals Suppose, for example, that you wanted to determine how the load voltage or current varied in response to different excitation signal frequencies in the circuit of Figure 61 An analogy could be made, for example, with how a speaker (the load) responds to the audio signal generated by a CD player (the source) when an ampli er (the circuit) is placed between the two1 In the circuit of Figure 61, the signal source circuitry is represented by its Th venin equivalent Recall that the impedance ZS presented by the source to the e remainder of the circuit is a function of the frequency of the source signal (Section 44) For the purpose of illustration, the ampli er circuit is represented by the idealized connection of two impedances, Z1 and Z2 , and the load is represented by an additional impedance, ZL What, then, is the frequency response of this circuit The following is a fairly general de nition:

The frequency response of a circuit is a measure of the variation of a load-related voltage or current as a function of the frequency of the excitation signal

Notice that your Solution Explorer window has been updated to include the new reference to the Web Service (see Figure 10-7).

VS CD Player (Source) Amplifier (Circuit) A physical system Speakers (Load)

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reality, the circuitry in a hi- stereo system is far more complex than the circuits that will be discussed in this chapter and in the homework problems However, from the standpoint of intuition and everyday experience, the audio analogy provides a useful example; it allows you to build a quick feeling for the idea of frequency response Practically everyone has an intuitive idea of bass, mid range, and treble as coarsely de ned frequency regions in the audio spectrum The material presented in the next few sections should give you a more rigorous understanding of these concepts

N Client-server (not multitier) Stand-alone 45 62 Min 12 10 P10 32 14 P25 55 29 Median 95 65 P75 153 119 P90 361 241 Max 498 491 Mean 134 97 Std Dev 119 95

According to this de nition, frequency response could be de ned in a variety of ways For example, we might be interested in determining how the load voltage varies as a function of the source voltage Then, analysis of the circuit of Figure 61 might proceed as follows To express the frequency response of a circuit in terms of variation in output voltage as a function of source voltage, we use the general formula HV (j ) = VL (j ) VS (j ) (61)

One method that allows for representation of the load voltage as a function of the source voltage (this is, in effect, what the frequency response of a circuit implies) is to describe the source and attached circuit by means of the Th venin equivalent e circuit (This is not the only useful technique; the node voltage or mesh current equations for the circuit could also be employed) Figure 62 depicts the original circuit of Figure 61 with the load removed, ready for the computation of the Th venin equivalent e

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Figure 10-7. The newly added Web Service reference displays in the Solution Explorer. 7. Double-click the Click To Calculate Area button on the Designer window to create an event-handling method for this button. Modify this button1_Click() event so that it looks like the following code:

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Fourier Analysis In this brief introduction to Fourier theory, we shall explain in an intuitive manner how it is possible to represent many signals by means of the superposition of various sinusoidal signals of different amplitude, phase, and frequency Any periodic nite-energy signal may be expressed by means of an in nite sum of sinusoids, as illustrated in the following paragraphs Consider a periodic waveform, x(t) Its Fourier series representation is de ned below by the in nite summation of sinusoids at the frequencies n 0 (integer multiples of the fundamental frequency, 0 ), with amplitudes An and phases n x(t) = x(t + T0 ) x(t) =

N Multitier Client-server (not multitier) 297 164 Min 08 11 P10 30 53 P25 50 81 Median 71 132 P75 126 216 P90 237 293 Max 609 618 Mean 108 160 Std Dev 103 109

One could also write the term 2 n/T0 as n 0 , where 0 = 2 = 2 f0 T0 (64)

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