Section B5: Circuit Analysis

We’ve spent a lot of time discussing the physical characteristics of a diode and the material/operational properties that are important. I’ll just say one more time... getting familiar with these concepts now will help immensely in our future studies – everything, absolutely everything, that we will be talking about with respect to electronic devices comes back to this material.

So, we’ve got the diode – what are we going to do with it? Well, we’re going to make them do something! For our purposes, we are going to concentrate on silicon (Si) based . Keep in mind that the general discussions still hold, with minor modifications as to physical constants, etc. The three analysis approaches we’re going to introduce are:

1. piecewise linear approximation; 2. graphical analysis; and 3. computer simulation techniques.

Piecewise Linear Approximation

The piecewise linear approximation to diode circuit analysis is based on the diode model of the previous section. Recall that, as long as the breakdown region of operation is avoided, the diode can be approximated as a controlled switch that is closed for vD > VON (where the diode is “on”) and open for vD < VON (where the diode is “off”). This technique allows us to replace the nonlinear device (the diode) with a simple representation that depends on the region of operation. These simplified representations were introduced in the diode models section and are reproduced below.

Sounds like a pretty good deal, doesn’t it? Well, there are a couple of potential problems:

1. Hand analysis of diode circuits often begins with the guess and check strategy as follows: a. Assume which state the diode is operating in (forward or reverse). b. Substitute appropriate model into circuit in place of diode. c. Analyze resulting circuit using standard analysis techniques. d. Check for contradictions (i.e., current flow in wrong direction or voltage polarity wrong) for state defined in step (a). e. If no contradictions, the original guess was correct. If something is not copasetic, go back, assume the other state for the diode and repeat the procedure. 2. If the circuit source(s) are simple dc, hand analysis is pretty easy (although it may be time consuming). If the source(s) in the circuit change, either through a defined time variation or other means, the diode may change state and analysis becomes more complicated.

Graphical Analysis

The graphical analysis technique may seem like way too much work for a simple diode circuit, but is used extensively in more complex circuits and for the devices introduced in the following chapters. For these reasons, we’re going to take a little while to introduce this analysis approach and the concept of operating point. The graphical analysis technique is based on the definition of two separate equations:

1. The representation of the nonlinear device of interest (here we’re talking about the diode). 2. The straight line, also called the load line that relates circuit parameters through standard linear analysis techniques.

These two equations are related through defined circuit parameters. Although it may be extremely difficult to solve for quantities of interest mathematically, graphically it is quite reasonable. The graphical analysis technique may be summarized as follows:

1. Plot each of the relevant simultaneous equations in the current-voltage (IV) plane. 2. Determine the intersection of the two curves. This intersection, defined as the operating point (also called the quiescent point or Q-point), determines the current and voltage parameters of the nonlinear device operation.

Figures 3.22 and 3.23 of your text illustrate this procedure with a simple series circuit that has a constant one volt source and one ohm series resistance. I would like to take a few minutes to repeat this analysis for a more general case (shown below). The circuit we’re going to look at is still a simple series, but now we have an arbitrary dc source VS, a series resistance R and a series connected diode. Using graphical analysis, we’re interested in solving for the series current ID and the diode voltage VD.

If we assume that the diode is forward biased, current will flow in the circuit as shown and we can proceed. The two relevant equations will be:

1. The forward biased diode equation (Equation 3.27 in dc terms):

vD

nVT I D = I 0e , and

2. The KVL circuit equation solved for ID:

V −V I = S D . D R

Once we have the simultaneous equations, we can plot them in the IV plane to get the operating point. The diode equation is pretty straightforward, but let’s look at how to get a quick-and-dirty sketch of the straight line by looking at the extreme cases for ID and VD in the circuit equation above.

¾ If ID is equal to zero, there is no drop across R and VD=VS. This will define the horizontal axis intercept. ¾ If VD is equal to zero, the entire source voltage will be dropped across R and ID=VS/R. This will define the vertical axis intercept. ¾ The resulting load line will be a straight line with a slope of –1/R.

Now we’ve got everything we need to complete the graphical analysis of this circuit, and it’s all put together in the figure to the right. The diode curve (in red) is the plot of the forward biased diode equation and the load line (in blue) is the result of the above analysis. The Q-point (aka quiescent point or operating point) is the intersection of the two curves and defines the operational parameters ID and VD.

While this may seem much ado about nothing, this is one of the techniques we will use to define the operational characteristics of future (more complicated) devices in terms of and maximizing design requirements – so hang in there!

Computer Simulation

The last analysis technique we’re going to introduce is that of computer simulation. Using simulation software, the circuit of interest may be entered as a schematic and/or through a netlist definition. Circuit elements – sources, linear and nonlinear components – are characterized through device models contained in the software and any required definitions (i.e., magnitude of sources, , etc., frequency of operation...). Several types of analyses may be run simultaneously in a single simulation, with the output represented graphically and/or through an output file.

The MICRO-CAP simulation software has been included with your text. While this is a very valuable tool and I strongly encourage you to become familiar with it, most of our examples will be performed using PSpice. If you wish, a free student copy of the PSpice software may be obtained, either as a download or by ordering an evaluation CD, from the Cadence website (http://www.pspice.com/download/default.asp). Tests, homework and design projects will be accepted using either of these simulation packages.

Just a note of caution... while computer simulation is the industry standard and virtually nothing is designed anymore without this approach, you must remember that it is just a tool! You absolutely must have a “feel” for what is happening and supposed to happen, or you will fall into the GIGO paradox that has trapped so many before! For this reason, and not just because I have completely gone over to the “dark side,” you will be required to present a theoretical analysis in addition to simulation results for most assignments in this sequence of courses.

The next part of this section is going to deal with something useful that the diode can actually do! Specifically, we’re going to talk about the concept of rectification in terms of half-wave rectification and full-wave rectification, and what we can do with this tool.