Performance Parameters

In this section, the expressions for the load current are first derived. Then an expression for the line current can be obtained. The r.m.s line current, the r.m.s. value of the fundamental of line current, the THD in line current, the frequency spectrum of line current, the frequency spectrum and the ripple content of the bridge output voltage and the frequency spectrum and the ripple content of the voltage across the load resistor are also determined.

For the case of discontinuous conduction, let the load current in each half cycle flow from q = a till q = p + b, where b < a. During this period, the differential equation that applies to the load current is calculated according to equation (6), where a is the firing angle, (p +b) is the extinction angle and the conduction angle within a cycle is (p + b - a ). The solution to the above equation is obtained as given shown in equation (7). In equation (7), t represents wL/R,the ratio of load reactance to load resistance. f is the load angle, defined to be tan^-1(wL/R). When the conduction is discontinuous, the load current starts from zero value at q = a. Hence equation (8) is obtained. When f < a , A has a negative value and we have discontinuous conduction when f < a . It means that the firing of the SCRs is retarded and a > f.

When the conduction is continuous, equation (9) applies. The solution to equation (9) is presented as equation (10). Since the signal applied to the load circuit is a periodic signal, the load current is also periodic, after a transient period. It means that equation (11) is valid for continuous conduction.

For continuous conduction, f > a and A is positive. When f = a, the conduction is about to become continuous and the value of A should satisfy both expressions for A. It is seen that f = a, A = 0 according to both expressions for A. When f = a , the current drawn from the source is sinusoidal and equals (E/Z)*Sin (wt - f), where Z is defined as shown in equation (12).

Once the load current is defined for a half-cycle, the expression for line current can be obtained. It equals the load current when SCRs S₁ and S₃ are conducting and it is the negative of the load current when the other pair of SCRs is conducting. Further analysis can be carried out using Fourier series and the DPF and PF of the line current can be determined.

When the circuit is switched on initially, the load current may settle down to a periodic response after a few output cycles. The time constant of the load is L/R and a time period corresponding to five times the constant should elapse before the load current becomes periodic. For example if the load time constant is 20 ms, a time period of 100 ms should pass before the load current becomes periodic. This time period corresponds to five input voltage cycles at 50 Hz and six input cycles at 60 Hz.

 
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