I'm trying to figure out what the input impedance to this op-amp circuit is. I have 2 ways I've been thinking about this, and I'm not sure which one is right, or if they're both wrong. I'm looking for the input impedance as seen by the AC voltage source, V1.
I posted an image of the circuit in question here:
Way 1: It's the impedances of C1, C2, and R3 in series. Done
Way 2: Thinking about a virtual short, it's C1, C2, R3, and R2 in series. Done
Basically, I'm wondering if R2 plays a role in the input impedance (as defined above) in this circuit.
Kinda what Jim said: at reasonably low frequencies the inverting input to the op-amp is a virtual ground, by virtue of the really high gain of the op-amp and the feedback through R4.
But once you approach the corner frequency of the circuit, which depends on the gain and the op-amp GBW product, then your input impedance will go up as the virtual ground starts looking like a virtual lossy inductor due to the feedback through the op-amp's low-pass nature.
Just where you have to start worrying about this depends on what you're doing with the circuit: if you need 16 bit precision then you need to start worrying at frequencies over 250 times lower than the circuit's corner frequency; if you aren't that desperate for precision then it's not that bad.
Why is there no virtual short? This is what I think is meant by the two terms
Virtual Short: the inverting and non-inverting inputs are both at the same voltage potential, essentially behaving as if they were shorted together.
Virtual Ground: if one input is tied to ground, then the other will also have a 0V with respect to ground, so even if it is not physically tied to ground it's still virtually tied to ground because of the other input.
neither input is tied to ground in my circuit. there's a DC voltage at the non-inverting and the AC signal at the inverting.
Since the non-inverting input only has a DC source on it, for any AC signal the voltage at the non-inverting signal is zero... hence the virtual ground. (...granted, there's a finite resistance between the "real" ground -- R1||R2 -- and the non-inverting input, but since the ideal op-amp input draws no current, there's no voltage drop and hence the non-inverting input is still a virtual ground.)
(In case this isn't clear: If you tell your multimeter to measure AC and hook it up to a DC power supply, the steady-state response is 0V.)
Think of it this way; the output of the opamp will do anything in it's power (i.e. be at whatever voltage within its rails) to make the voltage across its inputs zero. Since the '+' input is at a fixed voltage (not affected by the output voltage or the '-' input), it falls out of the AC equation. It's as if a battery were put at this point equal to the voltage at the '+' input.
It's not a short, rather a controlled voltage. V- is forced to be the same voltage as V+.
There is nothing magical about ground. Erase all your ground symbols (and connect those points together) and draw a ground at the '+' input. You've changed nothing.
Again, ground is a relative thing. You can define it to be anywhere.
The way you describe your "virtual short", current would have to flow from the non-inverting terminal, making it more like a _real_ short.
What really happens is that the op-amp does it's level best to make the inverting terminal voltage equal to the noninverting terminal voltage. It's _not_ a short in the sense that current going into the junction at the inverting terminal comes out the noninverting terminal. In a circuit like yours it becomes a virtual AC ground, or a virtual voltage source, or whatever other "virtual this or that" makes sense to you and still yanks the inverting terminal around to match the noninverting terminal voltage.
In my case (mid '80's) they taught plenty of fundamentals, just not much practical application. So there was lots of focus on filter bandwidth, but it was rare to have an exercise that let you figure out just how far down from a 3dB corner you had to be if you wanted less than 5 degrees phase shift, or accuracy within 0.01%, etc.
It _was_ easy to figure out once a senior guy pointed it out, but one did spend the first few years out of school smacking one's forehead and saying "d'oh".
(1) I grew up in a Radio & TV Repair Shop environment. (2) My father even provided me with an account at the parts wholesaler. (3) To meet college (MIT) expenses I had to work... from sophomore year on, as an electronics technician in an MHD lab, so I had lots of hands-on/soldering iron experience :-) (4) That MHD lab afforded me contact with real pros, like Jim Melcher (a PhD candidate at the time, later EE department head). Jim Melcher also taught a section on active circuit analysis. After one exam I proved to Melcher that not only had most of my classmates gotten an answer completely wrong (phase-plane trajectory), but so had he. He reversed all the grades... making me enemy #1 ;-) (5) I walked into Motorola SPD at the very beginnings of integrated circuits (MECL: Jan Narud, Walt Seelbach, Al Philips, Norm Miller and Art Capon, and me, their first analog guy :)... rolled my own from circuit design, breadboard, layout, cut Rubylith and shuttled everything thru the process line. (Got my MSEE courtesy of Motorola's "Training Program") (6) Shared a cubicle with Tom Frederiksen. We attacked each other's designs with a (friendly) vengeance... at a level of which Larkin would be brought to tears, or at least intense whining :-) (7) I even worked with George Wilson (Wilson mirror)... perfect asshole; and for Jim Solomon... intellectual thief who once claimed origination of the Gilbert Cell until the media cut him down ;-) (8) Mid '60's, Glen Madland and Howard Dicken leave Motorola and form ICE (Integrated Circuit Engineering), and I moonlight for them, writing their training course materials and giving seminars; then started doing custom I/C designs... thus I was thrust into custom designing... pretty much what I've stayed with ever since. (9) 1970, Got pissed at Motorola's attitude about blanket layoff's, refused to lay off any of my crew, laid myself off :-) (10) Joined Dickson Electronics the same day and started designing and building military hybrids. 4 of my 5 Motorola crew quit and joined me within a week. The 5th joined about 6 months later. (11) 1973, Got canned for moving my marketing aim from military toward commercial (and making more money :-) Went independent. (12) 1977-1987, I designed a custom chip for OmniComp (later consumed by GenRad) and went on staff. (13) 1987-????, Still knocking out about 3-4 chip designs per year ;-) (14) Stop working? Not a chance. I'd go nuts :-) ...Jim Thompson
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
Perhaps. Larkin takes poorly to criticism... can never admit error. Tom and I took it more as a learning experience... some of my best schemes came from Tom betting me I couldn't do it... like that NPN+lateral_PNP gimmick to make an essentially beta-independent PNP mirror... a cup of coffee bet ;-)
Then, one Friday, Tom claimed he could get 5-Watts out of an MC1554 Audio Amplifier (TO-5). I said no way. Monday I arrive to find that Tom had taken a block of Aluminum, machined a TO-5 sized hole with a clamp, drilled holes thru which he piped CO2... 5-Watts? No problem ;-)
No. But I knew Bob Rutherford who was VP... one call and I was hired.
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |