# gyrator

Joined Jan 19, 2004
220
i found the workin of an opamp gyrator on wikipedia..but the site didnt hav enough math to support the expression mention on the site
can anyone help me arrive at them..esp the actual expresson for Zin

#### Papabravo

Joined Feb 24, 2006
13,732
The expression for Zin is straightforward. To compute the parallel combination of impedances indicated by the double vertical line:
Rich (BB code):
Zin = (Z1*Z2)/(Z1 + Z2)
using the rules of complex algebra. Then the simplification is applied when R >> RL. So what's the problem?

Joined Jan 19, 2004
220
how are they in parallel?
virtual short circuit?

#### Papabravo

Joined Feb 24, 2006
13,732
The two nonzero impedances in parallel do not form a short circuit. In order for the result to be zero the product of Z1 and Z2 must be zero and the only way that can happen is if either Z1 or Z2 is equal to zero.

BTW what is a virtual short circuit? A circuit is either a short or it isn't, there is no "virtual" about it.

#### Dave

Joined Nov 17, 2003
6,970
BTW what is a virtual short circuit? A circuit is either a short or it isn't, there is no "virtual" about it.
Is it possibly in the context of virtual potential, as in the case at the inverting input to an op amp, i.e. virtual earth? Must agree I've not come across the term "virtual short" before.

Dave

Joined Jan 19, 2004
220
virtual short was meant with context to the fact tht both terminals of the opamp accquire (almost) the same potential owing to feedback.wrong usage of the term i must admitwat i m unable to see is how the author gets the combination in parallel with the other.. i cant see frm where the author got the expression for impeadance Z1(with refn to the above posts).

#### Papabravo

Joined Feb 24, 2006
13,732
OK, so the part you are missing is how they came up with the original expression for Zin. You are OK with the algebra to compute the parallel combination. Is this correct?

Joined Jan 19, 2004
220
yup..algebra is fine..

#### hgmjr

Joined Jan 28, 2005
9,029
yup..algebra is fine..

Here is my efforts at providing an analysis of the gyrator circuit you asked about in your initial posting.

You will see that I have made use of Millman's Theorem in the course of this analysis.

I would like to thank member joejester for his very valuable assistance in reviewing and checking the document's content. His feedback throughout its writing was critical.

Let me know if you have any questions.

If you encounter any problems opening this PDF file, try saving it to a folder on your local machine. That seems to work more reliably.

Gyrator Transfer Function Derivation

hgmjr

Joined Jan 19, 2004
220
thx a lot hgjmr and joejester

#### hgmjr

Joined Jan 28, 2005
9,029

Just let me know if you suspect that I have made any errors in my expression manipulations.

hgmjr

#### nomurphy

Joined Aug 8, 2005
567
BTW what is a virtual short circuit? A circuit is either a short or it isn't, there is no "virtual" about it.
Actually, there is no true "short" -- even a piece of wire has some resistance. A "short" is relative only to other circuit resistance or impedances.

If you were supposed to have a load of 1K, and the fuse on your power supply was popping, and you determined that the load was actually 10 ohms -- then you would have a "virtual" short circuit at your load. However, in other applications, the 10 ohms would not necessarily be considered a short.

If you wanted to bypass a circuit, you may add a wire jumper, or a resistor of some relatively low value (1, 10, 100 ohms) across the circuit that would then act as a "virtual" short because its impedance is much lower than the circuit impedance being bypassed.

#### Dave

Joined Nov 17, 2003
6,970
If you wanted to bypass a circuit, you may add a wire jumper, or a resistor of some relatively low value (1, 10, 100 ohms) across the circuit that would then act as a "virtual" short because its impedance is much lower than the circuit impedance being bypassed.
But is that really a "virtual" short? Virtual meaning that something exists or results in essence or effect, though not in actual fact, reference the decription at the op amp inputs given by haditya before. Surely by bypassing the circuit in the way you describe there is nothing "virtual" about that?

Dave

#### nomurphy

Joined Aug 8, 2005
567
"...exists or results in essence or effect, though not in actual fact..."

That is my point, a short is only a short relative to the desired impedance. A short does NOT in actual fact exist, for Zero ohms does not exist in everyday practice. All "shorts" are relative and virtual, a matter of symantics.

E.g., "I placed a diode across my co-phasing loop, and virtually shorted it out."

Now, if you want to talk about a DEAD short, that's something again.