Rectifier Instruments

RECTIFIER INSTRUMENTS

This instruments are used for the measurement of AC current and voltage. This uses rectifier element and a PMMC meter.

Rectifier element converts AC to DC. Peak inverse voltage of Germanium and silicon is 300v and 1000v respectively. Germanium is mostly used in rectifier type. instruments.

Half wave Rectifier:

If dc voltage is applied, V_dc = v and the full scale deflection current flows through the meter is given by,

I = V/(R_m + R_s) ……..(1)

If ac voltage is applied, V_ac = V_m  sinωt

= √2 V_rms  sinωt

= √2 V sinωt

where V = V_rms = root mean square value of applied voltage

V_m = peak value

This pulsating voltage produces pulsating torque. Due to the inertia of the moving parts, PMMC meter indicates a steady deflection corresponding to the average value of current.

average value of voltage = 1/2π ₀∫ ^π V_m sinωt dωt

= 1/π . V_m

= 0.318 V_m

= 0.318 (√2 V) = 0.45 V

 average current for full scale deflection, I = 0.45 V/(R_m + R_s) ………(2)

 Sensitivity of the instrument = 1/I_fsd

Where I_fsd. is the full scale deflection current.

and S_ac = 0.45 S_dc

Full wave rectifier circuit:

Average current through the PMMC meter is given by the average voltage, V_av.

V_av = 1/π ₀∫ ^π V_m sinωt d(ωt) = 2/π . V_m = 0.636 V_m

= 0.636 (√2 V_rms) = 0.9 V

Full scale deflecting average current, I = 0.9 V/R_m + R_s

Sensitivity of full wave rectifier = 2 (sensitivity of half wave rectifier)

and S_ac = 0.9 S_dc

Due to the Non linear nature of diode at the lower value, the meter scale is nonlinear at lower end, and gives low sensitivity at this region.

The scale, is calibrated in terms of rms value Average value of non sinusoidal waveform is differ from average value of sinusoidal waveform.

So calibrated scale gives error in its result for non sinusoidal waveform.

Extension of meter range:

To extend the range of a rectifier instrument which uses a PMMC meter, a series multiplier (R_s) is used.

For DC operation:

R_s = ﴾V/I_fsd﴿  - R_m - R_d

R_s = S_dc . V - R_m - R_d (for Half wave rectification)

and R_s = S_dc . V - R_m - 2R_d (for full wave rectification)

For Ac operation:

R_s = S_ac V - R_m - R_d (for half wave rectification)

and R_s = S_ac V - R_m - 2R_d

= 0.9 S_dc V - R_m - 2R_d (for full wave rectification)

Errors:-

1. Rectifier instruments are calibrated for sinusoidal waveforms, so non sinusoidal waveform causes error.

2. Non linear characteristics of diode cause error.

3. Temperature changes causes error.

4. Rectifiers act as imperfect capacitor and by passes high frequency current. This causes error.

5. Sensitivity lowers in ac operation. Rectifying elements are used for the measurement of average value of voltage with the help of the following circuit.