electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA chapter 10
Sinusoidal response of RC circuits When both resistance and capacitance are in a series circuit, the phase angle between the applied voltage and total current is between 0 and 90, depending on the values of resistance and reactance.
Impedance of series RC circuits In a series RC circuit, the total impedance is the phasor sum of R and XC. R is plotted along the positive x-axis. XC is plotted along the negative y-axis. R R Z is the diagonal XC XC Z Z It is convenient to reposition the phasors into the impedance triangle.
Impedance of series RC circuits Example Sketch the impedance triangle and show the values for R = 1.2 kW and XC = 960 W. R = 1.2 kW 39o XC = 960 W Z = 1.33 kW
Analysis of series RC circuits Ohm’s law is applied to series RC circuits using Z, V, and I. Because I is the same everywhere in a series circuit, you can obtain the voltages across different components by multiplying the impedance of that component by the current as shown in the following example.
Analysis of series RC circuits Example Assume the current in the previous example is 10 mArms. Sketch the voltage phasor diagram. The impedance triangle from the previous example is shown for reference. The voltage phasor diagram can be found from Ohm’s law. Multiply each impedance phasor by 10 mA. VR = 12 V R = 1.2 kW x 10 mA = 39o 39o XC = 960 W VC = 9.6 V Z = 1.33 kW VS = 13.3 V
Variation of 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. 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.
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. R VR Vout Vin Vout C Vin Vout Vin
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. C Vout Vin Vin R Vout Vout VC Vin
Applications An application showing how the phase-shift network is useful is the phase-shift oscillator, which uses a combination of RC networks to produce the required 180o phase shift for the oscillator. Amplifier Rf Phase-shift network C C C R R R
Frequency Response of RC Circuits When a signal is applied to an RC circuit, and the output is taken across the capacitor as shown, the circuit acts as a low-pass filter. As the frequency increases, the output amplitude decreases. Plotting the response:
Frequency Response of RC Circuits Reversing the components, and taking the output across the resistor as shown, the circuit acts as a high-pass filter. As the frequency increases, the output amplitude also increases. Plotting the response:
Selected Key Terms Impedance Phase angle Bandwidth RC Lag Circuit The total opposition to sinusoidal current expressed in ohms. The phase difference between source voltage and total current in a reactive circuit. The range of frequencies passed from input to the output of a circuit. A phase shift circuit where the output voltage lags the input voltage by its phase angle. The output voltage decreases as the input frequency increases.
Selected Key Terms RC Lead Circuit Frequency response Cutoff frequency A phase shift circuit where the output voltage leads the input voltage by its phase angle. The output voltage increases as the input frequency increases. In electric circuits, the variation of the output voltage (or current) over a specified range of frequencies. The frequency at which the output voltage of a filter is 70.7% of the maximum output voltage.
Quiz 1. If you know what the impedance phasor diagram looks like in a series RC circuit, you can find the voltage phasor diagram by a. multiplying each phasor by the current. b. multiplying each phasor by the source voltage. c. dividing each phasor by the source voltage. d. dividing each phasor by the current.
Quiz 2. A series RC circuit is driven with a sine wave. If the output voltage is taken across the resistor, the output will be in phase with the input. lead the input voltage. lag the input voltage. none of the above.
Quiz 3. A series RC circuit is driven with a sine wave. If you measure 7.07 V across the capacitor and 7.07 V across the resistor, the voltage across both components is a. 0 V b. 5 V c. 10 V d. 14.1 V
Quiz 4. If you increase the frequency in a series RC circuit, a. the total impedance will increase. b. the reactance will not change. c. the phase angle will decrease. d. none of the above.
Quiz 5. If you decrease the frequency in a series RC circuit, a. the total impedance will increase. b. the reactance will not change. c. the phase angle will decrease. d. none of the above.
Quiz 6. In an RC Lead Circuit, increasing the input frequency a. increases the output voltage. b. decreases the output voltage. c. increases the phase angle. d. none of the above.
Quiz 7. In an RC Lag Circuit, increasing the input frequency a. increases the output voltage. b. decreases the output voltage. c. increases the phase angle. d. none of the above.
Quiz The cutoff frequency of an RC circuit can be expressed as a condition when: a. its resistance is equal to the reactance b. fc = 1/(2RC) c. its output voltage is 70.7% of its maximum value d. all of the above
Quiz 9. The range of frequencies passed from input to the output of a circuit is called the a. bandwidth b. cutoff frequencies c. rejecting frequencies d. limiting frequencies
Quiz 10. When power is calculated from voltage and current for an ac circuit, the voltage and current should be expressed as a. average values b. rms values c. peak values d. peak-to-peak values
Quiz Answers: 1. a 2. b 3. c 4. c 5. a 6. a 7. b 8. d 9. a 10. b