Analysis of circuits containing diodes

[[email protected]]

Hi,

For the past couple of weeks I've been working through a book called
"Network Analysis" by M.E. Van Valkenburg. Specifically, I've learned
how to use Mesh/Nodal Analysis and Laplace Transforms to analyze simple
circuits. I'm pretty amazed at the power of these techniques (thank
you, Mr. Heaviside), even though I still have to learn more about
differential equations and other things.

Anyway, the book doesn't cover semiconductor components, and I would
like to know how you would perform Nodal/Mesh Analysis on circuits that
contain diodes. Is it difficult to do this type of analysis? I'm
hoping to apply these techniques to a voltage doubler circuit to help
me understand how it works, but I can't really do that without knowing
how to address diodes.

Thank you very much for your help!

 

[David Harmon]

On 23 Jan 2006 16:41:19 -0800 in sci.electronics.basics,
[email protected] wrote,

Anyway, the book doesn't cover semiconductor components, and I would
like to know how you would perform Nodal/Mesh Analysis on circuits that
contain diodes. Is it difficult to do this type of analysis?

http://home.comcast.net/~stager21/Circuits.html

Essentially you have to try twice. once using the equation for a
forward biased diode, and again for a reverse biased diode.
(At the risk of over-simplifying.)

 

[Noway2]

You need to determine what model of a diode will suit your purposes.
The most basic diode model is a current "valve" that lets current flow
only one way combined with a relatively fixed voltage drop. If this
simplified model does not provide enough accuracy for you, then you
will need to include the equations governing the behavior of the
device. The problem here is that the equations are non linear, often
times involving differentials, logrithms, and or exponentials, which
makes a closed form solution messy and difficult at best. My
suggestion to you would be that if you need this detailed of an answer
to resort to a computer simulation.

For starters, however, you could consult a book on microelectronic
circuits that covers diodes, transistors, etc.

 

[Guest]

[email protected] wrote:
: Hi,

: For the past couple of weeks I've been working through a book called
: "Network Analysis" by M.E. Van Valkenburg. Specifically, I've learned
: how to use Mesh/Nodal Analysis and Laplace Transforms to analyze simple
: circuits. I'm pretty amazed at the power of these techniques (thank
: you, Mr. Heaviside), even though I still have to learn more about
: differential equations and other things.

: Anyway, the book doesn't cover semiconductor components, and I would
: like to know how you would perform Nodal/Mesh Analysis on circuits that
: contain diodes. Is it difficult to do this type of analysis? I'm
: hoping to apply these techniques to a voltage doubler circuit to help
: me understand how it works, but I can't really do that without knowing
: how to address diodes.

: Thank you very much for your help!

Nodal Analysis is a technique that is applied to solve linear
circuits.

Diodes, BJTs, MOSFETs are non-linear elements, with multiple
regions of operation. In order to solve circuits containing these
elements, they must be replaced with linear models. The problem is that
they use a different linear model for different regions of operation.

A diode (to answer your initial question) can be modeled in one of
two regions of operation: Forward or reverse biased (let's ignore
avalance breakdown now, for simplicity.) A forward-biased
can be modeled as a voltage source with the value of the forward voltage
drop of the diode. A reverse biased diode can be modeled as an open
circuit.

To solve the circuit, you have to guess at which of the two
regions of operation the diode is operating in, replace the diode with the
appropriate linear model, and then solve the circuit with nodal analysis.
Once the circuit has been solved, you need to check to see whether your
guess was correct.

In the case of the diode, if you guessed forward-biased, but the
current through the diode was negative (i.e. flowing from cathode to
anode) when you solved the circuit, you guessed wrong -- forward biased
diodes necessarily must have positive current. Then you would re-solve
the circuit using the reverse-biased model. Conversely, if you guessed
reverse-biased, but found a voltage drop across the diode (modeled as an
open circuit) greater than the forward voltage drop of the diode, you
guessed wrong, because a diode with a large voltage drop (in the correct
direction) across it would be forward-biased. Therefore, you would
re-solve the circuit using the forward-biased model.

This process is identical for other non-linear elements, the only
difference is that the linearized models for those elements are more
complicated, and have more regions of operation.

Joe

 

[[email protected]]

Hi,

For the past couple of weeks I've been working through a book called
"Network Analysis" by M.E. Van Valkenburg. Specifically, I've learned
how to use Mesh/Nodal Analysis and Laplace Transforms to analyze simple
circuits. I'm pretty amazed at the power of these techniques (thank
you, Mr. Heaviside), even though I still have to learn more about
differential equations and other things.

Anyway, the book doesn't cover semiconductor components, and I would
like to know how you would perform Nodal/Mesh Analysis on circuits that
contain diodes. Is it difficult to do this type of analysis? I'm
hoping to apply these techniques to a voltage doubler circuit to help
me understand how it works, but I can't really do that without knowing
how to address diodes.

Thank you very much for your help!

Hi guys (David, Noway2, Joe),

Rather than clutter up the newsgroup, I thought I would just write one
thank-you to all of you.

So if I understand what I've read, if the voltage source was, say, a
square wave, the analysis could be even more complicated because the
diode's bias could also be a function of time. That sounds pretty
messy. Way over my head at this point. Simulation sounds like the
best route for me.

Thanks for your help!

 

[Guest]

[email protected] wrote:
: [email protected] wrote:
:> Hi,
:>
:> For the past couple of weeks I've been working through a book called
:> "Network Analysis" by M.E. Van Valkenburg. Specifically, I've learned
:> how to use Mesh/Nodal Analysis and Laplace Transforms to analyze simple
:> circuits. I'm pretty amazed at the power of these techniques (thank
:> you, Mr. Heaviside), even though I still have to learn more about
:> differential equations and other things.
:>
:> Anyway, the book doesn't cover semiconductor components, and I would
:> like to know how you would perform Nodal/Mesh Analysis on circuits that
:> contain diodes. Is it difficult to do this type of analysis? I'm
:> hoping to apply these techniques to a voltage doubler circuit to help
:> me understand how it works, but I can't really do that without knowing
:> how to address diodes.
:>
:> Thank you very much for your help!

: Hi guys (David, Noway2, Joe),

: Rather than clutter up the newsgroup, I thought I would just write one
: thank-you to all of you.

: So if I understand what I've read, if the voltage source was, say, a
: square wave, the analysis could be even more complicated because the
: diode's bias could also be a function of time. That sounds pretty
: messy. Way over my head at this point. Simulation sounds like the
: best route for me.

Yeah, for simple circuits, with simple input signals, it's
possible (and I'd recommend) going through the hand calculations to gain a
greater intuition of the circuit.

One thing that you might not be aware of (this is more applicable
for BJTs and MOSFETs, rather than diodes) is that there exists a
small-signal model. If your voltage source has a large DC bias with a
small AC signal, then a different linear model for the non-linear elements
could be employed to allow the circuit to be solved using nodal analysis,
etc. As long as the varying part of the signal is small, the small signal
approximations hold. However, for a large-signal input, like a full-scale
square wave, these approximations do not hold.

Simulators don't make these approximations. They use full-blown
nonlinear models for the nonlinear elements, (for a diode, Id =
Is*exp(vd*k) ) and use iterative methods to find the solution to the
circuit.

Joe

 

[Noway2]

The small signal model, around a linearized region, can be applied to a
diode as well. The analysis process is almost identical to that of a
BJT. The difference is that the diode will always attenuate the signal
where the transistor can amplify it.