Our first objective is to find out how to design the current-loop compensator G_sub_ci in the current control-loop of an average current-mode controlled converter. But to do so, we first need to understand transfer functions of average current mode controlled converters. In particular, we need to understand how changes or variations in a duty cycle D affect variations or perturbations in the current that we're interested in controlling. How do we actually establish the transfer functions of average current-mode controlled converters? We can rely on our knowledge of converter transfer functions with the duty cycle as the input. So d_hat represents a small signal perturbation in duty cycle. And through converter transfer functions that we have studied earlier, we can find out how that d_hat perturbation affects perturbations in the output voltage or, for example, inductor current. Now, to close the current control-loop around converter transfer functions that are based on the duty cycle d_hat as the small signal control input, we sense the inductor current through an equivalent current sensing resistance R_f. The sense signal is then compared to a reference or control input, we call V_sub_c, and the difference between the two is closest by the current-loop compensator G_sub_ci. The output of the current-loop compensator G_sub_ci is the signal that we call V_sub_m and the input of a pulse-width modulator. In a small signal model, the model of the pulse-width modulator is simply a gain. The gain being 1/V_sub_m, where V_sub_m is the amplitude of the sawtooth waveform in the pulse-width modulator. Finally, the output of the pulse-width modulator is the duty cycle perturbation d_hat. So this is in a block diagram form, a small signal model of a switching power converter that has average current mode control-loop around it. Notice that inside the control-loop, the control-to-output transfer function is no longer G_vd as we had in the voltage motor control converter, but instead is G_id. The response from d_hat to the current in this case i_L_hat. So G_id (S) plays the role of a control-to-output transfer function and that is the transfer function around which we will design the controlled loop including the current-loop compensator G_sub_ci. So, here is the complete control loop around an average current motor control converter. Let's look at the loop gain. We will refer to that loop gain as T_sub_i, i referring to that current control-loop to distinguish it from a voltage loop that we would refer to as T_sub_v later on. To find a loop gain T_i, let's identify the control loop. So, the control loop goes through the current-loop compensator, the pulse-width modulator, control-to-output transfer function, G_id, then through the sensor gain R_sub_f, and back to the point where we compare the sensed value to the control input, d_c_hat. So, T_sub_i is the loop gain for this control loop. And we can write down T_sub_i as the product of the gains along the feedback loop that is identified here. So, we will have R_sub_f , G_ic, 1/V_sub_m, and G_id. So, in this control loop, to loop gain is the one that you will use to design for a desired cross-over frequency and desired stability margins, such as phase margin, for example. Here is the feedback loop and the identified loop gain. So, to design the current control loop, the loop gain that we have just identified will play the central role. The first step will be to find the duty cycle to current transfer function, G_id, being d_hat input, i_L_hat output. Or, if we have some other current, other than inducted current that would be, in general case, some high hat, the current of interest. Then, we would proceed as we did earlier in designing voltage control loops. The plot magnitude and phase responses of the uncompensated current loop gain. The uncompensated current loop gain is simply the loop gain identified here with the G_ic, the current-loop compensator set to one. So, the uncompensated loop gain is simply the product of R_f, the gain of the pulse-width modulator, and the control to output transfer function, G_id. Based on the shape of the uncompensated current loop gain, we will determine the required shape of the current loop compensator transfer function, G_ic (S). And, we will do so, in order to achieve desired cross-over frequency and phase margin. In the next lecture we will illustrate the process using an example.