電子電路基礎(chǔ)課件CH3

1、Ch3 Basic RL and RC Circuits 3.1 First-Order RC Circuits 3.2 First-Order RL Circuits 3.3 Exemples Readings: Gao-Ch5; Hayt-Ch5, 6Circuits and Analog ElectronicsCh3 Basic RL and RC Circuits 3.1 First-Order RC Circuits Key Words: Transient Response of RC Circuits Time constant Ch3 Basic RL and RC Circu

2、its 3.1 First-Order RC Circuits Any circuit with a single energy storage element, an arbitrary number of sources, and an arbitrary number of resistors is a circuit of order 1.Any voltage or current in such a circuit is the solution to a 1st order differential equation.Ideal Linear CapacitorEnergy st

3、oredA capacitor is an energy storage device memory device.Ch3 Basic RL and RC Circuits 3.1 First-Order RC Circuits One capacitor and one resistorThe source and resistor may be equivalent to a circuit with many resistors and sources.R+-Cvs(t)+-vc(t)+-vr(t)Ch3 Basic RL and RC Circuits 3.1 First-Order

4、RC Circuits KVL around the loop:Initial conditionSwitch is thrown to 1Called time constant Transient Response of RC CircuitsCh3 Basic RL and RC Circuits 3.1 First-Order RC Circuits Time Constant RCR=2kC=0.1FCh3 Basic RL and RC Circuits 3.1 First-Order RC Circuits Switch is thrown to 2Initial conditi

5、onTransient Response of RC CircuitsCh3 Basic RL and RC Circuits 3.1 First-Order RC Circuits Time Constant R=2kC=0.1FCh3 Basic RL and RC Circuits 3.1 First-Order RC Circuits Ch3 Basic RL and RC Circuits 3.2 First-Order RL Circuits Key Words: Transient Response of RL Circuits Time constant Ch3 Basic R

6、L and RC Circuits 3.2 First-Order RL Circuits Ideal Linear Inductori(t)+-v(t)TherestofthecircuitLEnergy stored:One inductor and one resistorThe source and resistor may be equivalent to a circuit with many resistors and sources.Ch3 Basic RL and RC Circuits 3.2 First-Order RL Circuits Switch is thrown

7、 to 1KVL around the loop:Initial conditionCalled time constant Transient Response of RL CircuitsCh3 Basic RL and RC Circuits 3.2 First-Order RL Circuits Switch is thrown to 2Initial conditionTransient Response of RL CircuitsCh3 Basic RL and RC Circuits 3.2 First-Order RL Circuits Transient Response

8、of RL CircuitsCh3 Basic RL and RC Circuits Initial Value （t=0）Steady Value （t）time constant RL Circuits Source(0 state) Source-free(0 input) RCCircuits Source(0 state) Source-free(0 input)SummaryCh3 Basic RL and RC Circuits SummaryThe Time ConstantFor an RC circuit, = RCFor an RL circuit, = L/R-1/ i

9、s the initial slope of an exponential with an initial value of 1Also, is the amount of time necessary for an exponential to decay to 36.7% of its initial valueCh3 Basic RL and RC Circuits SummaryHow to determine initial conditions for a transient circuit. When a sudden change occurs, only two types

10、quantities will definitely remain the same before and after the change. IL(t), inductor currentVc(t), capacitor voltageFind these two types of the values before the change and use them as initial conditions of the circuit after change.Ch3 Basic RL and RC Circuits About Calculation for The Initial Va

11、lueiCiLit=0+_1A+-vL(0+)vC(0+)=4Vi(0+)iC(0+)iL(0+)3.3 ExemplesCh3 Basic RL and RC Circuits 3.3 ExemplesMethod 1(Analyzing an RC circuit or RL circuit)Simplify the circuit2) Find Leq(Ceq), and =Leq/Req ( =CeqReq)1) Thvenin Equivalent.(Draw out C or L)Veq , Req3) Substituting Leq(Ceq), and to previous

12、solution of differential equation for RC (RL)circuit .Ch3 Basic RL and RC Circuits 3.3 ExemplesMethod 2(Analyzing an RC circuit or RL circuit)3) Find the particular solution.1) KVL around the loop, the differential equation 4) The total solution is the sum of the particular and homogeneous solutions

13、.2) Find the homogeneous solution.3.3 ExemplesMethod 3 (step-by-step)(Analyzing an RC circuit or RL circuit)1) Draw the circuit for t=0- and find v(0-), or i(0-)2) Use the continuity of the capacitor voltage, or inductor current, draw the circuit for t=0+ to find v(0+), or i(0+)3) Find v( ), or i() at steady state4) Find the time constant tFor an RC circuit, t = RCFor an RL cir