Chapter 13: RC & RL Circuits - University of Massachusetts ...

1 Chapter 13: RC & RL Circuits Instructor: Jean-Fran ois MILLITHALER. Learning with Purpose Slide 1. Impedance & Admittance Element Impedance Admittance = 1. =.. = 1. = . 1 = . =.. Learning with Purpose Slide 2. RC Circuit I= Determine the source voltage and the phase angle. Draw the impedance triangle. 1 1 1. = + = = 104 = 104 ( 103 ). 2 103 10 8. = + = 10k = . = 2 + 2 = . k . = 1 = . 10k . = = = V. Learning with Purpose Slide 3. Variation of phase angle with frequency Phasor diagrams that have reactance phasors can only be 1. drawn for a single frequency because = is a function . of frequency. As frequency changes, the impedance triangle for an RC circuit changes as illustrated here because XC decreases with increasing f. This determines the frequency response of RC Circuits . Learning with Purpose Slide 4.

2 Frequency response Learning with Purpose Slide 5. Frequency response Frequency response of the low-pass RC circuit Learning with Purpose Slide 6. Frequency response Cutoff Frequency 1. =. 2 . Learning with Purpose Slide 7. applications For a given frequency, a series RC circuit can be used to produce a phase lag by a specific amount between an input voltage and an output by taking the output across the capacitor. This circuit is also a basic low-pass filter, a circuit that passes low frequencies and rejects all others. Learning with Purpose Slide 8. applications Reversing the components in the previous circuit produces a circuit that is a basic lead network. This circuit is also a basic high-pass filter, a circuit that passes high frequencies and rejects all others. This filter passes high frequencies down to a frequency called the cutoff frequency.

3 Learning with Purpose Slide 9. Learning with Purpose Slide 10. RL Circuit The current is 200 mA. Determine the source voltage. 2 = 2 10 kHz 100 mH = k . The impedance is = (10 k )2 +( k )2 = k . k . = 1 = . 10 k . Applying Ohm's law yields = = 200 A k = V. Learning with Purpose Slide 11. Phase Relationships of the Current and Voltages Example Determine the source voltage and the phase angle The source voltage is the phasor sum of VR and VL. = 2 + 2 = 502 + 352 = 61 V. The phase angle between the resistor voltage and the source voltage is 35. = tan 1 = tan 1 = 35o 50. Learning with Purpose Slide 12. Phase Relationships of the Current and Voltages 2 2 1.. = + = tan . Learning with Purpose Slide 13. Variation of Impedance and Phase Angle with Frequency Phasor diagrams that have reactance phasors can only be drawn for a single frequency because X is a function of frequency.

4 As frequency changes, the impedance triangle for an RL circuit changes as illustrated here because increases with increasing f. This determines the frequency response of RL Circuits . Learning with Purpose Slide 14.