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

-V

The aim is to obtain V

**Kirchhoff's**voltage law to the circuit,-V

_{f }- I_{f}R_{L}+ V_{in }= 0The 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

The point A gives y intercept while point B gives x intercept of the line.

_{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 |

_{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**

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