Diode Circuits 1CHAPTER 2 DIODE CIRCUITS As discussed in the previous section, diodes are essentially one-way valves. They carry current in one direction, but block current in the other. In addition, in the forward conduction mode, the voltage must go above a threshold before significant conduction occurs. Diodes are used in a multitude of ways that utilize these characteristics. The objective of this course is not to look at hole and electron flows, but to see how the diodes can be used in circuits and how to analyze those circuits. For example, consider the circuit below, Figure 1. We are generally not interested in the holes and electrons in the diode, but rather, the current in the resistor or the voltage across the resistor. Figure 1. A simple diode circuit NUMERICAL METHOD The diode being a non-linear element means that the basic methods of circuit analysis learned in your circuits course cannot be used. Then, how does one go about analyzing the circuit? For example, we can write a loop equation Vs = Vd + Vr = Vd + I*R Unfortunately, there are two unknowns in this equation, I and Vd. The relationship between voltage and current in the diode is given by IIeVVDT=−01()() Where VT is 25.9 mV at 300 degrees K, and IO is the reverse saturation current. If we put the two equations together we get VVRIeSdVVDT=+ −01()() (1) This equation cannot be solved analytically. But it can be solved numerically. You can make a guess of the diode voltage and plug into the equation and see if you get a balance.Diode Circuits 2If not, try another guess. This process can be carried out several ways. The simplest is to use a calculator, while more complex methods would use a computer. One interesting approach is to use a math solving program on a personal computer such as MathCAD. Literally all circuits could be solved this way, but that would be impractical, especially for more complex circuits. Secondly, the diode equation mentioned above only represents the hole-electron currents within the body of the diode. There is a considerable leakage on the surface of the semiconductor which makes the low current solutions in error. GRAPHICAL METHOD Instead of using the diode equation as the model, we can get quite satisfactory results by using simpler models, or by using graphical methods from the plotted V-I characteristic of the diode. Consider the circuit in Figure 2. The loop equation is Vs = Vd + I*R (2) a. b. Figure 2. Diode circuit to be solved graphically If we divide the circuit as shown in Figure 2b, the equation can be rewritten to solve for the voltage at the division. Vd = 5 - I*R (3) This equation can be solved for current IVRd=−5 (4) This equation represents the relationship between current and terminal voltage for the left-hand side of the circuit. The relationship between current and terminal voltage for the right-hand side is just the equation for diode. IIeVVDT=−01()() (5)Diode Circuits 3Each of these equations is just an I vs Vd equation and can be plotted on a graph. Equation 4 is a linear equation and its plot is called the load line. It can easily be plotted by selecting values for Vd and calculating I. For example, the two intercepts; Vd = 0 and I = 0 are convenient choices. The equation 5 is the diode I vs V characteristic for the diode. It is usually obtained from a curve tracer in the laboratory. Both of these equations are plotted on the same graph in Figure 3. The operating point for the circuit is where the two plots cross. 510−=−VRIedVVDT()() (6) Figure 3. Plots for graphical solution One problem with the graphical solution above is that the voltage scale is so large that precision in determining diode voltage is difficult. In many cases, the diode characteristic is plotted with a much lower maximum voltage than the voltage source in the circuit. In this case, the voltage intercept is off the scale and it is more difficult to plot the load line. This situation is easily handled by substituting in a fixed value of voltage in the load line equation and solving for the current. An example is shown in Figure 4. The maximum voltage on the diode characteristic plot is 2 Volts with the source voltage 5 Volts and a resistance of 1KΩ. Solving the load equation IRmA=−=523 which gives us the current at Vd = 2 volts at the right hand end of the load line on the plot in Fig. 4. Figure 4. Diode Characteristic and Graphical Solution CIRCUIT MODELS The graphical method presented in the previous section is one possible method of solution of circuits with diodes. For obvious reasons, this method will get very tedious and time consuming for more complex circuits. What we would like to do is to find a way to solve the circuits analytically; with equations. We do this by using circuit models which are combinations of ideal circuit elements that behave the same or almost the same as the actual device. We then solve the circuit using standard methods of circuit analysis.Diode Circuits 4A model is what we use to represent an actual device. For example, we use a mathematical expression V=IR to represent the voltage across a resistor. This happens to be a very good model at low frequencies, below a few MHz. At higher frequencies, the inductive reactance becomes significant and the equation is no longer very accurate. Similarly, V = jωLI and I = jωCV are good models for inductors and capacitors at relatively low frequencies. We also use models for voltage and current sources. For example, a typical voltage source is far from ideal. It usually has internal resistance and cannot supply unlimited current. Now let us take a look at what these ideal circuit models represent. If we draw a plot of the relationship between current and voltage of a resistor, we get the plot in Figure 5a. Similarly if we plot the I-V characteristic of the ideal voltage source, we get the plot in Figure 5b. The I-V characteristic of the voltage source in series with the resistor is shown in Figure 5c. a. Resistor b. Voltage source c. Series combination Figure 5. Models for a Resistor and a Voltage Source Circuit Models for Diodes. Now let's look at possible circuit models we can use for a diode.