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SingleTimeConstant Circuits Fculty Personal Homepage 单一时间常数电路教师个人主页.doc

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SingleTimeConstant Circuits Fculty Personal Homepage 单一时间常数电路教师个人主页

Single-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers. Objectives To analyze and understand STC circuits with emphasis on time constant calculations To identify different STC configurations: low pass and high pass To study the switching performance of the STC circuits Introduction Circuits that are composed of, or can be reduced to, one reactive component and one resistance are known as single-time-constant (STC) circuits. Time Constant (τ) is defined as the time required to charge a reactive element (capacitor or inductor) to 63 percent (actually 63.2 percent) of full charge or to discharge it to 37 percent (actually 36.8 percent) of its initial value. For an RC circuit, the value of one time constant is expressed mathematically as τ = RC. For RL circuit τ = R/L. The importance of the STC is appreciated, when we know that the analysis of a complex amplifier circuit can be usually reduced to the analysis of one or more simple STC circuits. Time Constant Evaluation The first step in the analysis of an STC circuit is to evaluate its time constant ?. Example 1: Find the time constant of the circuit shown in Figure 1. Fig-1 in (Lec_01_Ver_01.vsd) Figure 1 STC circuit for example 1. Solution: Apply Thévenin’s theorem to find the resistance seen by the capacitor. The solution details are as follow: Step 1: Apply Thévenin’s theorem to the circuit contains R1, R2, and vI to obtain Rth1 and Vth1 as shown in Figure 2.. Fig-2 in (Lec_01_Ver_01.vsd) Figure 2 First reduction to the STC in Figure 1 using Thévenin’s theorem. Rth1 is calculated by reducing vI to zero. That means both R1 and R2 will have the same two nodes. . Vth1 is the open circuit voltage across R2 which may be calculated using voltage division. (Vth1=vI*R2/(R1+R2) Step 2: The STC in Figure 1 may be simplified using Thévenin’s circuit in Figure 2 to obtain the simplified circuit in Figure 3. Fig-3 in (Lec_01_Ver