Exercise 7 – AC voltage measurements – peak responding detectors

1. Aim of the exercise

The aim of the exercise is to familiarize students with the AC voltage measurements by means

of peak responding detectors.

2. Main topics

Issues with AC voltage characterization

Basic principles of peak responding detectors (AC and DC coupled) .

Design of peak responding AC voltmeters.

3. Gained skills

Oscilloscope observation of the input and output signals of AC and DC coupled peak

responding detectors,

Designing peak-responding AC voltmeters,

Characterization of peak-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∫ [𝑢(𝑡)]2

𝑡0+𝑇

𝑡0

𝑑𝑡

- Rectified average voltage – a mean of the absolute value of the signal voltage:

𝑈𝐴𝑉 =1

𝑇∫ |𝑢(𝑡)|

𝑡0+𝑇

𝑡0

𝑑𝑡

- Peak value:

𝑈𝑀 = |𝑢(𝑡)|<𝑡0,𝑡0+𝑇>max

- Peak to peak value

𝑈𝑃𝑃 = 𝑢(𝑡) − 𝑢(𝑡) <𝑡0,𝑡0+𝑇>min

<𝑡0,𝑡0+𝑇>max

Based on these values several useful factors can be defined:

- Form factor:

𝑘𝑓 =𝑈

𝑈𝐴𝑉

- Crest factor:

𝑘𝑐 =𝑈𝑀

𝑈

For sine (harmonic) signal:

𝑘𝑓 =𝜋

2√2≅ 1,11

𝑘𝑐 = √2

Peak responding detectors

The electric diagrams of peak responding detectors are presented in figure 1.

Figure 1. Peak responding detectors a) DC coupled, b) AC coupled.

The basic principle of both types of detectors is that a diode allows the capacitor to be

charged, but prevents its discharging (as a diode is component which allows only one current

direction). In terms of their topology the AC and DC coupled detectors are the same, their

difference is only due to the different set-up of the output (from the capacitor in the DC coupled

and from the diode in the AC coupled).

To comprehend the operation of the detectors it is useful to bear in mind that due the

Kirchhoff’s Voltage Law, the directed sum of the electrical voltages around any closed network

is zero and it applies each single moment. The phenomena are illustrated in figure 2.

Figure 2 Principle of operation of peak responding detectors.

Besides of the voltage, an important parameter of the peak responding detector is its low

limiting frequency. In this task it is assumed as:

Fd10=10/(R·C)

Laboratory module description

Module P01 (Figure 3) makes it possible to investigate a peak responding detectors in both AC

and DC coupled set-ups. Diode and capacitor should be connected in an arbitrary configuration

in the “Przetwornik” block of the module. When connecting a diode one needs to take care on

their polarization (connection direction). In this purpose, taking a look at the figure 4 is advised.

Figure 3. P01 Module

Figure 4. A diode

Anode Katode

5. Measurements and tasks

Task 1. Investigation of the performance of DC coupled peak responding detector Using P01 build a DC coupled peak responding detector. Use the capacitor provided by the supervisor.

a) Set the sine input signal of Vpp of 5 V and frequency of 1 kHz. Connect this signal to the DC coupled detector input. For both diode polarizations observe both input and output signals on the oscilloscope. Use the same scale and the ground level for both the oscilloscope channels. Put the oscillograms in the report and comment on them.

b) For a single diode direction investigate the influence of the loading resistance on the shape of the output signal. In order to this connect the decade resistors to V connectors and shortcut Rd connectors. Put a few (distinctive) oscillograms in the report.

c) Add the DC offset to the input signal and repeat the observations from point a). Based on the obtained results discuss the observation. Address the differences between the obtained oscillograms and theoretical predictions and explain them.

Task 2. Investigation of the performance of AC coupled peak responding detector

Set the sine input signal of Vpp of 5 V and frequency of 1 kHz. Connect this signal to the AC coupled detector input. For both diode polarizations observe both input and output signals on the oscilloscope. Use the same scale and the ground level for both the oscilloscope channels. Put the oscillograms in the report and comment on them. Investigate the influence of adding a DC component to the input signal and comment on that.

Based on the obtained results discuss the observation. Address the differences between the obtained oscillograms and theoretical predictions and explain them.

Task 3. Design of a peak responding AC voltmeter

Design a peak responding AC voltmeter of the voltage range UZ and the low limiting frequency fd10 (which will be provided by supervisor) calibrated to measure the RMS value of sine waveform. Use LM-3 voltmeter of χ=1kΩ/V and the voltage range UZ0. Consider a diode as an ideal one. Calculate the resistance of Rd resistor (which should be connected in series with the LM-3 meter) and capacity of the C capacitor. Put the design data, voltmeter scheme together with formulas and calculations in the report.

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Task 4. Characterization of the designed peak responding AC voltmeter

a) Based on your design in task 3 build a peak responding AC voltmeter. Use 34450A AC voltmeter as a reference meter. Set the sine signal voltage from the generator to obtain UFS of the designed voltmeter on the calibrated meter. Set the frequency 3-5 times higher than fd10. Connect the signal to the meter you constructed and adjust Rd to have the full deflection. Put a new Rd value into the report with the frequency you applied. How the adjustment influenced the fd10? Calculate the new low limiting frequency.

b) Measure the designed voltmeter’s deflection vs input voltage characteristics =f(U) for the full range. In this purpose keep changing the input voltage from 0 to UFS with 0.5 V step and measure the input (reference) voltage (U) with the use of multimeter. is the designed voltmeter deflection in units. Draw the obtained dependency and compare it with the theoretical one (most suitably on the same drawing).

c) Set the RMS of the input voltage for UFS/2. Measure the output RMS of the designed voltmeter for a number of frequencies between 0.2 and 2 fd10. Based on the results draw a frequency characteristic of your meter.

Control questions

1. Why do we connect a resistor in series with LM-3 meter in the peak responding AC

voltmeter?

2. What is the role of the diode in peak responding detectors?

3. What is the role of the capacitor in peak responding detectors?

4. What is the frequency impact on the reading of peak responding AC voltmeters?

5. What is the loading resistance impact on the reading of peak responding AC voltmeters?

6. A DC coupled peak responding detector is supplied with sine signal of Vpp = 10 V and the

DC component of a) -2 V, b) 2 V. Draw the output signals for each diode polarization.

Consider the diode characteristic ideal and open circuit at the output.

7. A DC coupled peak responding AC voltmeter is supplied with sine signal:

u(t)=5+10sinωt [V]. What will be the reading if the meter is calibrated for the RMS

value? What would be the reading of a DC voltmeter for this signal?

8. An AC coupled peak responding AC voltmeter is supplied with sine signal:

u(t)=5+10sinωt [V]. What will be the reading if the meter is calibrated for the RMS

value? What would be the reading of a DC voltmeter for this signal?

9. Draw the output signals for AC and DC coupled peak responding detectors if they are

supplied with a signal: u(t)=5+10sinωt [V].

10. What resistance should be connected in series with a magnetoelectric meter of the

internal resistance of 10 kΩ and the voltage range of 10 V to obtain an AC voltmeter

calibrated to measure the RMS of the sine signal on the same voltage range. For the

voltmeter a peak responding detector was used.

11. What is the influence of the duty cycle of the rectangular waveform on the indication

of peak responding detectors? Draw sample signals for a DC coupled detector.

12. What problems can you expect with the measurements of low-voltage signals with the

use of peak responding detectors?