### Diode as a Circuit Element

Consider a simple diode circuit shown in the Fig. 1 in which a d.c. voltage of is applied to load resistance through a diode. The output is voltage across the resistance. Fig. 1  Simple diode circuit
Apply Kirchhoff's voltage law to the circuit,
-Vf - If RL + Vin = 0
The aim is to obtain Vf as well as the current I. Thus there are two unknowns and on equation.
The second equation is provided by the diode current equation as,
But solving these two equations is not easy due to an exponential term. The solution gives transcendental which can not be solved directly. Hence the graphical method is used to solve these equations.
1.1 Static Characteristics and the Load Line for a Diode
Applying Kirchhoff's voltage law to the circuit,
Now we have two unknowns Vf and If and only one equation. The second equation is the equation of forward characteristics of the diode which is an exponential equation. But analytically, solving these two equations is difficult hence graphical analysis is used.
For graphical analysis, the diode forward characteristics as given in the datasheet specifications, is considered. This is known to us. On this characteristic, equation (1) is drawn.
The equation (1) is a straight line equation, which gives linear equation (1) between Vf and If. This equation is called equation of d.c. load line for the diode.
Note : The load line is always straight line.
Sketching d.c. load line : According to equation (1), obtain the two points.
Point A, Vf = 0 hence If = Vin/RL according to equation (1)
Point B, I= 0 hence V= Vin according to equation (1)
The point A gives y intercept while point B gives x intercept of the line.
The line joining the points A and B is called d.c. load line of the diode.
Sketch this line on the forward characteristics of the diode. The forward characteristics already exists as per the diode datasheet specifications. The combined graph is shown in the Fig. 2.
1.2 Q Point
The relation between Vf and If is predefined for the device interms of its forward characteristic, given in the datasheet of the diode.
For the given circuit conditions, Vf and I relationship is given by the d.c. load line.
Note : Thus there exist only one point on the d.c. load line as per the forward characteristics of the diode. It is the intersection of the forward characteristics and d.c. load line of the diode. This is called operating point, quiescent point or Q point of the device.
It is also called d.c. biasing point for the diode.
Remember that practically points A and B may be not achieved. The point A and B are theoretical points used to sketch the d.c. load line. The practical operating point is the Q point.
Rearranging the equation (1),
It can be sen that slope of the line is -1/RL i.e. reciprocal of the load resistance RL. Hence the line is called a load line.
Note : The slope can be controlled and operating point Q can be adjusted as per the requirement by varying resistance RL.
1.3 Calculating Load Resistance and Supply Voltage
It is seen that Q point can be adjusted by changing the values of RL or supply voltage Vin.
Similarly for a given Q point, the supply voltage Vin and load resistance RL can be obtained.
For a given Q point, first load line is drawn through point B(Vf = Vin) and Q point. The slope of this line is (-1/RL). Thus knowing the slope of d.c. load line, load resistance can be obtained.
Similarly if Q point and RL are known then the d.c. load line can be drawn having slope (-1/RL) ans passing through Q point. The intersection of this line with x-axis gives the value of the the supply voltage Vin.
The graphical method is little bit complicated but gives the accurate results. The response of the diode circuit can be predicated using the concept of d.c. load line and the graphical analysis. The method of d.c. load line is commonly used to analyse complicated diode circuits and the variety of electronic circuits.
1.4 Practical Difficulty and its Solution
One practical difficulty may arise while sketching a d.c. load line. The value of I = Vin/RL for Vf = 0 may be high such that it may not be available on the current scale on y axis. In such a case, any current I' is selected from the available scale and = Vin - I' RL is obtained. The point C(Vf' , I') is obtained. and d.c. load line is plotted passing through points B and C, as shown in the Fig. 2. Fig. 2  Solution to practical difficulty

1.5 Dynamic Characteristics
The dynamic characteristics are important when the input voltage is varying. Let us study the procedure to obtain the dynamic characteristics.
Firstly a load line and static characteristics are plotted as explained earlier. Then let the current  IA is the current, corresponding to the intersection point A of load line with static characteristics. Plotting this current vertically above Vin, we get the first point of dynamic characteristics. Such a point B is shown in the Fig. 3.
Now if input is charged to  Vin' then new load line is to be obtained with points (0, Vin'/RL)  and (Vin' , 0). The slope of the load line remains same. So this load line will be parallel to the earlier load line. The corresponding intersection point with static characteristics is A' and IA' is the current corresponding to it. Plotting this current vertically upwards Vin', we get the second point of dynamic characteristics B' as shown in the Fig. 3. Fig. 3  Dynamic characteristics

1.6 Transfer Characteristics
The graph showing the variation of output voltage Vo with input voltage Vin of any circuit is called transfer characteristics of that circuit. These are also called transmission characteristics.
For the basic diode circuit considered earlier, the output voltage Vo = i RL, thus it is directly proportional to the current. Hence graph of Vin against Vo will have same shape as the graph of Vin against i. Thus the shape of transfer characteristics is same as that of dynamic characteristics of the circuit.
The use of transfer characteristics is to obtain graphically the resultant output waveform for varying input voltage, at low frequencies. This is shown in the Fig. 4.
The input waveform is drawn with time axis vertical while voltage axis horizontal parallel to x-axis. Consider triangular input waveform.
Let a instant t = t', the input is denoted at point A. The corresponding input is VinA. The corresponding output can be obtained from transfer characteristics by projecting intersection of  VinA with transfer curve, on y-axis. The corresponding output is VoA. This is plotted separately against the time axis. The procedure is to be repeated for various points such as B, C, D as shown, the corresponding outputs are shown as b, c, d in the Fig. 4. Fig. 4  Use of transfer characteristics

As long as Vin  is less cut-in voltage Vγ, the diode will not conduct and output will be zero.
Thus    V = 0 V                 for   Vin  < Vγ
So for points E, F, G etc. of input voltage, the output is zero.
The corresponding portion of input will not appear at the output and will get clipped off. Thus diode acts as a clipper. The complete method is illustrated in the Fig. 4.
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