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,
            -V_f - I_f R_L + V_in = 0

       The aim is to obtain V_f 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 V_f and I_f 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 V_f and I_f. 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, V_f = 0 hence I_f = Vin/R_L according to equation (1)

       Point B, I_f  = 0 hence V_f  = 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 V_f and I_f is predefined for the device interms of its forward characteristic, given in the datasheet of the diode.

       For the given circuit conditions, V_f and I_f  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/R_L i.e. reciprocal of the load resistance R_L. 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 R_L.

1.3 Calculating Load Resistance and Supply Voltage

       It is seen that Q point can be adjusted by changing the values of R_L or supply voltage Vin.

       Similarly for a given Q point, the supply voltage Vin and load resistance R_L can be obtained.

       For a given Q point, first load line is drawn through point B(V_f = Vin) and Q point. The slope of this line is (-1/R_L). Thus knowing the slope of d.c. load line, load resistance can be obtained.

       Similarly if Q point and R_L are known then the d.c. load line can be drawn having slope (-1/R_L) 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/R_L for V_f = 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' R_L is obtained. The point C(V_f' , 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  I_A 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  V_in' then new load line is to be obtained with points (0, V_in'/R_L)  and (V_in' , 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 I_A' is the current corresponding to it. Plotting this current vertically upwards V_in', 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 V_o with input voltage V_in 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 V_o = i R_L, thus it is directly proportional to the current. Hence graph of V_in against V_o will have same shape as the graph of V_in 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 V_inA. The corresponding output can be obtained from transfer characteristics by projecting intersection of  V_inA with transfer curve, on y-axis. The corresponding output is V_oA. 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 V_in  is less cut-in voltage V_γ, the diode will not conduct and output will be zero.
       Thus    V_o  = 0 V                 for   V_in  < V_γ
       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.

Solved examples on diode as a circuit element