Recent content by Jmf

The assumption that the voltages at the inverting and non-inverting inputs are equal only holds when the op amp is working in it's usual operating region (i.e. output not saturated to +9 or -9V). That's my understanding, anyway, since we usually assume negligible output impedance and a large...

I'm not sure about an algorithm for solving this problem in general - but unless I misunderstood the problem then you're solving: A^k = I for A = [2,3;3,5] and k some integer? I'm pretty sure that a solution doesn't exist, as the values of the matrix will grow without bound as k goes large.

Oh, sorry - I didn't see that it says -6A on the diagram, I thought it was 6A. I think I've seen an error though - in the equation for node 1, 0.5 should be 0.1 I think? since two 0.2 ohm resistors in parallel give a resistance of 0.1 ohm between nodes 1 and 2.

Sorry, but that's just not true. There is current through D2 and D1, since the 10mA current must be shared between D1 and D2, and thus there is a voltage drop across both D1 and D2. It's not an easy problem, actually, since there are two nonlinear elements. You can write down a few different...

Can you upload Fig. 4.26? Without seeing the circuit I can't say for certain, but you may be able to use the diode equation if you know the leakage current, temperature etc. Or you may be able to solve graphically with a 'load line' if you have a plot of the diode characteristic.

Sure; I'll just do the equation for node 1, then I can go into some detail. And I'll use the currents out of the node, since that's what you've learned: by Ohm's law, the current going from node 1 to power supply 1 is: \frac{v_1 - 10}{4 700} note that I put v_1 first and 10V second...

Yeah, that's exactly what I meant. :)

I did something very similar recently for an experiment in control engineering. The system is actually nonlinear, and gives rise to equations like: A_1 \dot{h_1} = Q_{in} - Q_1 A_2 \dot{h_2} = Q_1 - Q_{out} where: Q_1 = \sigma_1 A_1 \sqrt{2g(h_1 - h_a)} Q_{out} = \sigma_2 A_2 \sqrt{2g(h_2 -...

A sign error: your equation for node 1 is correct, but the one for node 2 should be +6 at the start, not -6. (look at the direction of the current source in the circuit).

Apologies if I go into too much detail, but I think that sketching the proofs of convergence of each method actually helps a lot to understand why they work: If, for the system Ax=b, you express A as the sum of upper triangular, diagonal, and lower triangular matrices, then both Gauss-Siedel...

I haven't done the analysis myself (I will if you would like to see it, since you've obviously made a good attempt at the question) but I believe there are sign errors in your equations. When doing node analysis, you're applying Kirchoff's Current Law, so for each node you can write, for...

Implementations of circuits like this can vary somewhat, but I'll reference the diagram you gave: C1, C2 and the inductor should determine the frequency of oscillation. Normally getting an accurate frequency is important, so these will probably be one of the more accurate types of capacitors...

I believe you are correct with 2 ohms, but I'm not so sure about your reasoning. Assuming a 1V voltage source is a good thought - then the voltages at each point are determined. Instead of thinking about resistors in series or parallel, apply basic circuit laws - specifically Ohm's law will...

So we have: f(x,y) = xy e^{-(x+y)} (I hope that's correct, I wasn't sure how to read your e^-x-y) I think the derivatives of this are: \frac{\partial f}{\partial x} = y(1-x)e^{-(x+y)} \frac{\partial f}{\partial y} = x(1-y)e^{-(x+y)} Which is similar to what you have, except the sign...

I study control engineering rather than mathematics, but: Taylor's theorem, in all it's forms (one variable, multiple variables, complex variables, using vectors/matrices, with and without the bounds on the error. etc) since I think it's useful in so many different contexts. Lots of people...