An equivalent circuit of a device is a combination of elements suitably connected so as to best represent the actual characteristics of the device.
Different diode equivalent circuit models are piecewise linear circuit model, simplified equivalent diode model and the ideal diode model.
The most accurate equivalent circuit model for a diode is the piecewise linear equivalent circuit model.
The simplest equivalent circuit model for a diode is the ideal diode circuit model.
In this model the diode curves are represented by straight-line segments. Figure below shows the model and its V-I characteristics.
This model makes an assumption that the diode will not conduct until the voltage at the anode exceeds the cathode voltage by the cut-in voltage. Therefore, a battery voltage (VB) having a magnitude equal to the cut-in voltage of the diode, has been introduced in the circuit opposite to the conduction direction of the diode. When the applied voltage across the diode exceeds VB, the diode starts conducting. The resistance of the diode is expressed as the dynamic-ON resistance (rd) in the forward-biased condition.
Piecewise linear equivalent model of a diode
The line drawn in the equivalent model curve has a slope equal to the inverse of the value of the dynamic resistance (1/rd). The diode shown in the model is an ideal diode which acts as a short circuit in the forward bias direction and as an open switch in the reverse bias direction.
However, it does not result in the actual duplication of the diode characteristics, especially in the knee region. Also, the model is equally valid for both DC as well as AC applications.
When the network resistance is much larger than the value of the diode resistance (rd), then a simplified model as shown in the figure below can be used. Here the diode resistance is assumed to be zero. The model makes an assumption that the in the forward biased condition, the diode will not conduct until the cut-in voltage is reached and after that it acts as an ideal closed switch. The diode does not conduct in the reverse bias condition.
Simplified equivalent diode model - 1
When the applied voltage is much greater than the diode’s cut-in voltage then the model shown below is used. Here, the curve has been approximated by a straight line through the origin and the slope of the straight line is given by the inverse of the static diode resistance at the point of intersection of the line with the diode V-I characteristics.
Simplified diode equivalent model - 2
In the ideal diode model, the diode acts like a perfect closed switch with zero ON resistance and as a perfect open switch with infinite OFF resistance. Figure below shows the V-I characteristics of an ideal diode model. This model is applicable when the applied voltage levels are much larger than the diode’s cut-in voltage and the network resistance is of a much larger value than the diode’s dynamic-ON resistance.
V-I characteristics of an ideal diode model
Load-line analysis is a graphical method of analyzing a circuit. Here, a load line is drawn on the actual characteristic curve or on the equivalent model curve of the active device used in the circuit. It provides very accurate results when the actual characteristic curve of the active device is used for analysis. Load line analysis can be done for both DC and AC applied voltages.
Perform the load line analysis for this circuit.
Simple diode circuit with DC input voltage
Applying Kirchhoff’s voltage law to the circuit, we get
Where,
VD is the diode voltage
ID the diode current
The straight line represented by the above equation is called the load line. The two variables, VD and ID, are the same as the diode’s V-I characteristic axis variables. Therefore, a second relationship between the two variables is given by the V-I characteristic curve of the diode. The intersection of the load line with the V-I characteristic curve of the diode determines the operating point of the circuit also called the quiescent point or the Q-point.
The load line can be drawn by determining its intercepts on the voltage and the current axis. For VD = 0, ID = VI/R and for ID = 0, VD = VI. The straight line joining these two points is the load line. The slope of the load line is given by –1/RL. Figure below shows the load line analysis for a diode circuit for DC input voltage. The operating point for the circuit is (VDQ, IDQ), where VDQ = VDD – IDQ RL.
Load-line analysis of a diode circuit for DC input voltage
Perform the load line analysis for this circuit.
Simple diode circuit with AC input voltage
Since the input voltage applied is time-variant, separate load lines need to be drawn for the instantaneous values of the input voltage. Since, the value of load resistor (RL) is fixed, the different load lines are parallel to each other. The intersection of these lines with the static V-I characteristic curve of the diode, gives the value of the current in the circuit corresponding to different instantaneous values of the input signal.
Another better method to determine the current is to draw the dynamic characteristic curve of the circuit. It is also a plot between the diode current and the input voltage. Refer to figure below. The load line for the maximum value of the input signal is drawn. From the Q-point a horizontal line is drawn. The point where this line intersects with the vertical line drawn from the X-axis corresponding to that input voltage gives a point on the dynamic curve. The process is repeated for a few other values of input voltage to yield sufficient points to construct the dynamic curve.
Dynamic characteristic curve for the circuit given in the question
If a triangular waveform as shown in Figure below is applied to the circuit, then the dynamic curve can be used to draw the output current waveform.
Input waveform
Refer to Figure below. It shows how the dynamic curve can be used for plotting of current waveform.
Output waveform construction of a diode circuit for AC input voltage