Single Phase Half Wave Controlled Rectifier with R Load

In this article, we will see the analysis of Single Phase Half Wave Controlled Rectifier with Resistive (R) Load as shown in Figure 1. V_s is supply and ‘i_s‘ is the source current. V_T and ‘i_T‘ is the SCR voltage and current respectively. V_o and ‘i_o‘ is the load voltage and current respectively.

V_s = V_msin(ωt)

Step-1: Write KVL in the given circuit

v_s − v_T − v_o = 0

v_ab = v_s = v_T + v_o

v_ab = v_s = V_msin(ωt)

v_ba = − v_ab = − V_msin(ωt)

Step-2: Device working status

In the positive half cycle, SCR is forward biased and is turned ON at ωt = α by giving a firing pulse (triggering pulse). The angle α is called delay angle or firing angle. It is measured from the instant the SCR has become forward biased.

At ωt = π, the current through the SCR falls to zero i.e. below zero and simultaneously a reverse voltage appears across SCR and it turns OFF. Since the line voltage is used for commutation, it is also known as line commutation converter.

1). 0 < ωt < α

SCR is in forward blocking mode and SCR is OFF.

i_o = i_s = i_T = 0 Amp

v_o = 0 V

v_T = v_ab = V_msin(ωt)

2). α < ωt < π

SCR is in forward conduction mode and SCR is ON.

v_T = 0 V

i_o = i_s = i_T = (V_msin(ωt))/R

v_o = v_ab = V_msin(ωt)

3). π < ωt < 2π

SCR is in forward blocking mode and SCR is OFF.

i_o = i_s = i_T = 0 Amp

v_o = 0 V

v_T = v_ab = V_msin(ωt)

4). 2π + α < ωt < 3π

SCR is in forward conduction mode and SCR is ON.

v_T = 0 V

i_o = i_s = i_T = (V_msin(ωt))/R

v_o = v_ab = V_msin(ωt)

The waveforms for load voltage(v_o), and current(i_o), SCR voltage(v_T) is shown in figure 2. The waveforms of supply current and SCR current is same as load current.

Note: For a resistive load, v_o and i_o waveform will be same in nature except in magnitude.

Step-3:

1). Firing angle (α) = α

2). Extinction angle (β) = π

3). Conduction angle (γ) = β − α = π − α

4). Conduction time (t_c) = γ/ω = (π − α)/ω

5). Circuit turn off time (t_ckt-off) = (2π − π)/ω = π/ω

6). Peak Inverse voltage (PIV) = V_m

Step-4:

Average Values

The average output voltage V_o(avg) across load R is given by

The average output current I_o(avg) through the load R is given by

RMS values