Operation of the half-wave rectifier with active - inductive load and limited inductance

Figure 1.5

L_d is connected in series with a load for smoothing a rectified current.

Equivalent resistance and inductance of a circuit are

According to second Kirchhoff’s law

where

Characteristic equation is

From here

We should search out solution as i=i_ss+i_fr; where i_fr – a free component, i_ss - a steady state component.

Where

Constant A we could be found from initial conditions:

At

Then

from here

Let's designate

Then

Figure 1.6

Let's find the energy reserved in inductance L by period

Energy which inductance accumulates

Energy which inductance takes out

Thus, in the time of period

A direct component of the rectified voltage is

where l - a pulse load current duration.

A direct component of a rectified current is

It is possible to determine λ from the condition: at u = λ Þ i_d =0

If L_d would increase, λ also increases and I_dm goes down, hence, K_r decreases. Thus, it is possible to use L_d as the filter of a load current.