What types of circuits give rise to Singular martices?

Do you mean like using matrix math to solve simultaneous differential eqautions. I think simple filter circuits would fall into that category.

I sometimes get an error in spice (ltspice) that a matrix is singular, I doubt this is quite the same as you are wanting though is it ? Its usualy when ive shorted out something.

Colin =^.^=

The classic op-amp circuit for making a variable output impedance, which includes some positive feedback, is singular at output impedance equal infinite. One regularly sees designs that work around the singularity; Horowitz and Hill, _The Art of Electronics_ 2ed fig 4.94L is one such. Model that one with Rsmall equal to zero, and the effect of any small deviation (like .001 % of a resistor value) turns the output impedance negative...

Thank you for your replies. I was actually looking for simple example of circuits like Filter circuits and also as mentioned circuits (with a short). I just want circuit such that when i enter them as netlist, the matrix formed by them should be singular.

Thanks, dilip

EdV wrote:

A circuit on the verge of oscillation should have a system matrix which is near singular. And oscillators with the gain element adjusted to have exactly the gain needed for oscillation. For instance, the classic R-C phase shift oscillator; see

Set the amplifier gain to exactly -29 and that should give you an example of what you're looking for.

That's clear enough :-)

As people say, many classic filters have this property. Basically, some circuits (even a few passive circuits) have either oscillations (ideal oscillators, e.g. an L and a C component in parallel with no resistive loss) or undefined solutions (these are also singularities in the matrix).

For the undefined solutions, classic examples are circuits with capacitor cutsets and inductor loops. An inductor loop is self-explanatory (examples include LC filters with transmission zeros). Capacitor cutsets are nodes connected only to capacitors, i.e. with no DC path to ground. These are undefined at DC, and will make standard Spice complain. There are also circuits with undefined solutions at inifinite frequency[1].

As such, a simple example is two capacitors in series where the voltage in the middle is undefined at DC.

Hope this helps

Jens

circuits

To expand on the 'undefined solutions' case, consider Schmitt triggers, or the classic Eccles-Jordan flip-flop; they are bistable and that means two equally valid solutions for some input values, i.e. the matrix will be singular. Not all cases with undefined solutions are pathological, they can be useful as latches or self-starting oscillators.