Deciding Vout, switches/digital

beggi9

Joined Mar 3, 2016
42
In all of these equations, are (x_a) and (x_b) Boolean values (i.e., either a 0 or a 1)?
So I can simply take out (x_a) and (x_b) right? and the answers to the four senarios would be:
When (x_a) is to Vref and (x_b) to ground: Vut = (3/4)*Vref

When (x_a) is to ground and (x_b) to Vref: Vut = (1/2)*Vref

When both (x_a) and (x_b) are to Vref: Vut = (3/4)*Vref

When both (x_a) and (x_b) are to ground: Vut=0

Or are my calculations wrong?

WBahn

Joined Mar 31, 2012
25,297
You are close. Ask if all of your answers make sense. In particular, if both switches are to Vref you say that the output is (3/4)*Vref. Now you switch (x_b) to ground and you are saying that doing so has no effect on the output. Does that make sense?

beggi9

Joined Mar 3, 2016
42
You are close. Ask if all of your answers make sense. In particular, if both switches are to Vref you say that the output is (3/4)*Vref. Now you switch (x_b) to ground and you are saying that doing so has no effect on the output. Does that make sense?
Ohh yeah I did a mistake when (x_b) is to ground and (x_a) is to Vref.
It should go Vut = Vref-6*I2*R=2*I2*R

so Vut = (1/4)Vref
right?

WBahn

Joined Mar 31, 2012
25,297
That's what I expect -- I haven't actually cranked the math.

Have you learned superposition yet?

beggi9

Joined Mar 3, 2016
42
That's what I expect -- I haven't actually cranked the math.

Have you learned superposition yet?
No I haven't, but I read about it briefly now and I can see how you caught my error

WBahn

Joined Mar 31, 2012
25,297
No I haven't, but I read about it briefly now and I can see how you caught my error
I didn't use superposition. I caught your error exactly as I described it -- by asking if the answers make sense.

1) Always, always, ALWAYS track your units.

The reason that I mentioned superposition is that problems like this really lend themselves to it. Plus, not only do you get an answer much quicker, but you can build up the general case answer very easily so that if someone tells you the switch positions you can almost immediately tell then the output voltage.

beggi9

Joined Mar 3, 2016
42
I didn't use superposition. I caught your error exactly as I described it -- by asking if the answers make sense.