Complex waveforms are most accurately measured with a true rms reading voltmeter. This instrument indicates the rms value of any waveform (such as a sine wave, square wave or sawtooth wave) by using an rms detector that responds directly to the heating value of the input signal.
To measure the rms value of an arbitrary waveform, we may feed an input signal to a heating element in close proximity to a thermocouple as shown in Fig. 5.12.
Recall that a thermocouple in a junction of two dissimilar match whose contact potential in a function of the temperature of the junction. The heater raises the temperature of the thermocouple and produces an output voltage that is proportional to the power delivered to the heater.
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The value of k in equation (ii) depends on the distance between the heater and the thermocouple and on the materials used in the heater and thermocouple. The difficulty with this method is that the thermocouple often displays a nonlinear characteristic. This problem is over come in some instruments by placing two characteristic.
This problem is over come in some instruments by placing two thermocouples in the same environment as shown in Fig. 5.12. The nonlinear characteristic of the input measuring thermocouple is cancelled by similar nonlinear effects of the balancing the rms couple in the feedback circuit. The two thermocouples form part of a balanced bridge applied to the input circuit of a dc amplifier. The ac input voltage is applied to the heater of the measuring thermocouple. An output voltage V1 is produced that upsets the balance of the bridge. This unbalance of the bridge.
This unbalanced voltage is amplified by the dc amplifier and fed back to the heater of the balancing thermocouple. When the output of both thermocouples in equal, bridge balance will be re-established. Thus, the dc feedback current is equal to the ac current in the input thermocouple. This dc current in therefore directly proportional to the rms value of the input voltage and indicated on the dc voltmeter in the output circuit of the dc amplifier. To verify this one distance that,
k0 = A(v1 – v2) …(iii)
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where A is the voltage gain of the dc amplifier. Rearranging equation (iii), we get;
k1 – v2 = k0/A ≈ 0 …(iv)
When A is a very large number for a high gain amplifier. Therefore;
k1 ≈ v2 …(v)
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From equation (v), it is clear that,
Kv2rms = kv02
or vrms = k0
The voltage measure by the dc voltmeter in approximately equal to the rms value of the input signal. Hence we have on rms voltmeter. The true rms value in measured independently of the waveform of the ac signal, thus the waveform of the input signal is immaterial. If the ac input voltage is very small, an ac amplifier may be used to increase the signal level before applying it to the input thermocouple. Sensitivities in the millivolt region are possible with such an arrangement.
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A typical laboratory type rms-responding voltmeter provides accurate rms reaching of complex waveforms having a crest factor (ratio of peak value to rms value) of 10/2. At 2 percent of full scale meter deflection, where there is a change of amplifier saturation, waveforms with crest factors as high as 100/1 could be accommodated. Voltages throughout arrange of 100 mV to 300 V within a frequency range of 10 Hz to 10 MHz may be measured with most good instruments.