Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
Thank you, Tony.op amp works simply by using as much gain as available to ensure the differential input is zero.
Since the inverting input has two sources the original input and the output via passive components, both must add up to zero or whatever voltage is on (+) side.
The attenuation from the output to (-) is what controls the gain and ends up being just the Z impedance ratio of the -Zfb/Zin(-) or in the simplest case -Rf/Rin
Thank you, audioguru. The graph you provide involves a lot of knowledge inside.Your graph should look like this:
Thank you very much, MrAl. I have repeated all the calculations of the three gains for open-loop, voltage follower and the general non-inverting configuration, I'm glad I have the same expressions as yours. More importantly, when I substitute the dc gain of the follower or the non-inverting into the open-loop gain expression to find the corresponding frequency, the frequency happens to be the -3dB bandwidth of corresponding configuration! That gives a direct proof of what crutschow said and the graph audioguru gave in post #141, at least a proof for those two configurations.Hi,
The open loop or closed loop gain can be calculated for the original simple LT Spice model:
Measured External Open Loop Gain=(Aol*GBW)/sqrt(GBW^2+Aol^2*f^2)
Non Inverting Closed Loop Gain of 1=(Aol*GBW)/sqrt((Aol^2+2*Aol+1)*GBW^2+Aol^2*f^2)
The non inverting closed loop gain is for a voltage follower connection.
To get the gains in db, take the log base 10 and multiply that by 20 (as usual).
Note that the gain of 1 op amp configuration starts out with a gain of 0db at f=0 and ends at -3db at f=GBW.
For a general connection non inverting gain of A we have:
Vout=(Aol*A*GBW)/sqrt((A^2+2*Aol*A+Aol^2)*GBW^2+Aol^2*f^2*A^2)
where A is the circuit gain due to some external resistors, so we get circuit gains such as 1, 5, 10, etc. The external resistors should be greater than 100 ohms, preferably 1k or greater.
Again take the log base 10 and multiply that by 20 to get the gain in db.
If you draw a horizontal line at a particular closed-loop gain, then where it intercepts the open-loop plot is the circuit bandwidth at that gain.
Thank you very much, MrAl. I have repeated all the calculations of the three gains for open-loop, voltage follower and the general non-inverting configuration, I'm glad I have the same expressions as yours. More importantly, when I substitute the dc gain of the follower or the non-inverting into the open-loop gain expression to find the corresponding frequency, the frequency happens to be the -3dB bandwidth of corresponding configuration! That gives a direct proof of what crutschow said and the graph audioguru gave in post #141, at least a proof for those two configurations.
This time, I consider the inverting configuration:Hi,
Here is a quick plot of the op amp with three different gain settings (with external resistors) using the equation with the gain factor in it. In this diagram G represents the gain setting with the external resistors.
Noteworthy is that the DC gain for an external gain setting of 100000 does not make it all the way to 100db because the internal gain stage has a gain of only 1e5. With a gain of 1e6 it would come closer.
Thank you, MrAl.Well if we factor the -3db down frequency point we get:
fcutoff=GBW*(G/Aol+1/Aol+1)/(G+1)
and we can immediately see that when Aol is large and G much lower, this approximates to:
fcutoff=GBW/(G+1)
and we can see that for low G, G becomes comparable to that "1" in the denominator, so we end up with a lower frequency because that '1' is not insignificant.
G is the external circuit gain set with the two external resistors.
If I want to evaluate the inverting amplifier's frequency relationship with output voltage Vout, the inverting terminal voltage Vn, the circuit's gain or its cutoff frequency, taking the internal R and C into consideration, I use the following circuit and superposition, that's all I know. How do you define the 'error voltage'?The physical reason for this might be because the error voltage at the inverting terminal is lower than what it is with a non inverting configuration so that the internal gain is not as effective with a gain of 1. In the non inverting config, the output connects directly to the inverting input so there's no divider action. We could look into this more...you could look at the inverting terminal error voltage and see what you can spot...in other words, find out what causes that extra gain loss at a gain of 1 or 2.
I just want to congratulate all the posters in this thread. This has got to be one of the best threads I've seen in a homework section, and I mean crossed all the forums I've visited in the last 20 years.. Keep up the good work Heidi, as you epitomize what a good student does with a resource like this. I can tell you've learned a lot from this thread and I've enjoyed seeing your growth. I can see you paying this forward as time goes on.
Congrats everyone. Keep up the good work.
Thanks, JoeJester. Thanks to all the experts helping me, I did learn a lot which I didn't obtain in class.
Thanks again!
Hello MrAl,So what i would suggest is that for a given input like 1v, you calculate the output voltage, vn voltage, and the voltage at the output of the internal gain stage Aol before the RC filter, and see what you can find out. Note that because we are dealing with AC signals you may have to include the phase shift of each node too, probably with respect to Vin's phase which we can consider to be zero.
The most likely frequencies to look at would be 5 Hz and below, or something like that, because that is where the discrepancy begins to show itself.
G F Vout Db Ph
--- ------ ----- ---- -----
1 1000 1.00 0.0 179.9
1 10000 1.00 0.0 178.9
1 100000 0.98 -0.2 168.7
1 1000000 0.45 -7.0 116.6
1 10000000 0.05 -26.0 92.9
2 1000 2.00 6.0 179.8
2 10000 2.00 6.0 178.3
2 100000 1.92 5.6 163.3
2 1000000 0.63 -4.0 108.4
2 10000000 0.07 -23.5 91.9
5 1000 5.00 14.0 179.7
5 10000 4.99 14.0 176.6
5 100000 4.29 12.6 149.0
5 1000000 0.82 -1.7 99.5
5 10000000 0.08 -21.6 91.0
10 1000 10.00 20.0 179.4
10 10000 9.94 19.9 173.7
10 100000 6.73 16.6 132.3
10 1000000 0.91 -0.9 95.2
10 10000000 0.09 -20.8 90.5
[/FONT]