Exercise 7 AC voltage measurements average responding voltmeters 1. Aim of the exercise The aim of the exercise is to familiarize students with the AC voltage measurements by means of rectified average responding detectors. 2. Main topics Issues with AC voltage characterization Basic principles of rectified average responding detectors (half- wave and full-wave). Design of rectified average responding AC voltmeters. 3. Gained skills Oscilloscope observation of the input and output signals of rectified average responding detectors, Designing rectified average -responding AC voltmeters, Characterization of rectified average -responding AC voltmeters. 4. Brief introduction AC signal parameters - RMS (Root Mean Square) U voltage which is equal to the value of the direct current that would produce the same power dissipation in a resistive load. Can be expressed as: U = 1 T t 0 t 0 +T [u(t)]2 dt - Rectified average voltage a mean of the absolute value of the signal voltage: U AV = 1 t 0 +T T u(t) dt t 0 - Peak value: U M = max <t 0,t 0 +T> u(t) - Peak to peak value max <t 0,t 0 +T> min U PP = u(t) u(t) <t 0,t 0 +T> Based on these values several useful factors can be defined:
- Form factor: - Crest factor: k f = U U AV k c = U M U For sine (harmonic) signal: k f = π 2 2 1,11 k c = 2 Laboratory module description Module P02 (Figure 1) makes possible to investigate half-wave and full-wave rectifiers. To build a half-wave rectifier one needs to connect a diode into the D slot in the PJ 1 block. To use the full-wave rectifier one needs simply to choose it by a switch on the board to take signal from the PD block. The full wave rectifier is built with the use of the bridge connection and is equipped with the transformer which makes it possible to observe both input and output signals. Input signal needs to be connected to the GEN socket. Input observation is possible with the use of the OSC on the left side. After selecting by a switch a PJ or PD block, the output signal can be observed by the OSC on the right (after short-circuiting the Rd slot, which further will be used for building a voltmeter for connecting a decade resistor). R0/mA slot is used for connecting loading resistance in first part of the experiment and further to build a voltmeter. Figure 1 P02 Module 1 PJ and PD are Polish abbreviations for half-wave and full-wave rectifiers
The schemes of AC voltmeters based on a half wave and full wave rectifiers are given in Figure 2. a) R d b) u(t) ma u(t) R d ma Figure 2. AC average responding voltmeters based on a) half-wave b) full wave rectifiers
Measurements and tasks Task 1. Observation of input and output signals of half and full wave rectifiers The common settings for the experiments in this part are as follows: - Rd slot should be short-circuited, - as a loading a 10 k resistor should be connected to R0/mA. - Each of the oscilloscope channel (allowing for observation of input and output should have the same settings and be DC coupled). - Set the wave at the waveform generator to sine and frequency to 1 khz - The generator output should be set in the high input resistance mode. Task 1.1 Half-wave rectifier a) Set the Vpp at the waveform generator to 6 V (no offset), f = 1 khz. Observe the signals on the PJ block input and output for both diode D directions and put them into the report. Compare the oscillograms of the waveforms for the case of the ideal rectifier. How the polarity of the diode affects the shape of the output signal? b) Investigate the influence of the Vpp on the output signal by observing the inputs and outputs for Vpp of 1 V, 2 V and 6 V (sinusoidal signal, f = 1 khz). Put the waveforms in the report and comment on them. Note the difference between the amplitude of the input signal and the maximum voltage on the output for each case. Comment on the obtained results. Compare the obtained oscillograms with the waveforms for the case of an ideal rectifier. What is the reason of the observed differences between the input signal amplitudes and the maximum values of the output signal? Task 1.2 Full-wave rectifier a) Set the Vpp at the waveform generator to 6 V (no offset). Observe the signals on the PD block input and output and put them into the report. Comment how the waveforms differ from those expected for ideal diodes? b) Investigate the influence of the Vpp on the output signal by observing the inputs and outputs for Vpp of 1 V, 2 V and 6 V (sinusoidal signal without offset, f = 1 khz). Put the waveforms in the report and comment on them. Note the difference between the amplitude of the input signal and the maximum voltage on the output for each case. Compare the results with those obtained in task 1.1b
Comment on the obtained results. Compare the oscillograms with the waveforms for the case of an ideal rectifier. What is the reason of the observed differences between input signal amplitudes and the maximum values of the output signal? Task 2. Design and examination of the average responding AC voltmeter calibrated for measuring RMS of sine wave signals. a) Design an average responding AC voltmeter calibrated for measuring RMS of sine wave signal of a given UFS (in RMS value, remember) provided by supervisor. Use full-scale rectifier PD. Full scale current IFS and internal resistance of the LM-3 miliammeter will be provided by the supervisor as well. Assume an ideal characteristic of diodes. (When designing the device base on Figure 2 and bear in mind that for a given UFS on the circuit input the decade resistor (Rd) should ensure the current (of a mean value) equal to the IFs of the miliammeter.) Include in the report the scheme of the designed voltmeter, together with calculations. Sketch theoretical conversion characteristic = f(urms_input) b) Connect the LM-3 to R0/mA and the decade resistor to Rd in the set-up to build the voltmeter you designed, take care if you properly set PJ (half-wave) or PD (full-wave) with the switch. c) Adjust Rd to obtain full deflection at the LM-3 for a given RMS value of input voltage. Put the new value into the report. In the report give the pointer deflection of LM-3 miliammeter (in divisions) before and after adjustment of Rd. d) Measure, put into a table and sketch the characteristics = f(u) where is a deflection of your LM-3 meter [div] and U is the reference input voltage measured by the AC voltmeter (34450A). In order to that change the input voltage (i.e. RMS) in range from 0 to UFS with step of 0.5 V. Use the measurement set-up shown in Figure 3. Comment on the non-linearity in the obtained characteristics. How the non-linearity of the characteristic depends on the UFS? R d G V P ma Figure 3. Measurement circuit for the AC voltage examination
Control questions: 1. Draw the block diagram and explain functions of a AC voltmeter. 2. Give the definition of the average value of AC signal. 3. Give the definition of the RMS of AC signal. 4. What is the average value of the signal given by equation u(t) = -2 4 sin(200t)? 5. What is RMS of the signal given by equation u(t) = 2 + sin(10t)? 6. The waveform shown in the figure below was recorded for 1 V/div. What is the average value of the signal? 7. What will be the DC voltmeter s reading if it measures the signal shown in the figure below? 8. Give the definition of the form factor and its value for the sine wave. 9. Draw the current voltage characteristic of an ideal and real silicon diode. Mark the important points. 10. Draw the signals on the input and output of a half wave rectifier provided that the input signal is given by equation u(t) = -2 + 3sin(t). Assume an ideal diode characteristics. 11. Explain the operation of a half wave rectifier by drawing input and output voltage signals in the circuit. Assume the threshold voltage of the diode U D = 0V and its resistance in conduction direction R D = 0. 12. A sine signal of the amplitude of 10 V and 0 V offset was supplied to a full wave rectifier. What will be the indication of the ammeter of the internal resistance of 1 connected to the rectifier output in series with a 99 resistor in case if you assume a) ideal diode characteristics b) a silicon diode with U D = 0.6 V? 13. Explain if the diode polarization direction influences the reading of the rectifier based AC voltmeter if it is supplied with a sine signal with 0 offset. Justify your answer.