Here's one that does seem to meet the problem's requirements (except that the rolloff isn't exactly a single pole .....):

View attachment 91972

That's an interesting circuit.
Okay, here's a little brain teaser.
Is that close to the maximum theoretical flat bandwidth (no peaking) you can get with a gain of 2 inverting op amp compensated for a GBW of 1MHz?

 

That's an interesting circuit.
Okay, here's a little brain teaser.
Is that close to the maximum theoretical flat bandwidth (no peaking) you can get with a gain of 2 inverting op amp compensated for a GBW of 1MHz?

I'm not sure there is a theoretical limit. With the ideal components LTSpice lets you use I'm already over 5MHz.

 

Unless there are more poles above the GBW, which there usually are, there's no limit to how high you can raise the cut-off.

Regards

 

I'm not sure there is a theoretical limit. With the ideal components LTSpice lets you use I'm already over 5MHz.

Post your circuit and simulation, please!

 

Unless there are more poles above the GBW, which there usually are, there's no limit to how high you can raise the cut-off.

The limit is economics. From your wallet for the hobbyist, to the price someone is willing to pay for your design.

 

Post your circuit and simulation, please!

It's clearly not practical, just an interesting Gedankenexperiment.

It exploits the fact that the ideal op-amp model has zero output impedance, so it has infinite power gain at all frequencies even though the voltage gain rolls off. The transformer and R3 are used to crank up the input voltage to compensate for the dropping gain. The response is so flat as the ideal op amp model has a single pole rolloff to infinity, an ideal response which can be perfectly compensated over a reasonable range by the transformer circuit. As Russmax noted, real op amps have additional poles and there is usually considerably more phase shift than 90deg at the unity gain frequency.

I have made no effort to make the component values practical and have no idea whether it is possible to do so.

I suspect that practical techniques are limited to the types of peaking caps and chokes shown in earlier posts.

 

That's an non-inverting amp, not the inverting amp that we were talking about, but it's still an interesting circuit.

 

That's an non-inverting amp, not the inverting amp that we were talking about, but it's still an interesting circuit.

You confused me, referencing my non-inverting circuit and questioning the limit of inverting circuits. Guess you are interested in something like this:



What do you think the answer to your brain teaser is?

 

View attachment 92058

It's clearly not practical, just an interesting Gedankenexperiment.

It exploits the fact that the ideal op-amp model has zero output impedance, so it has infinite power gain at all frequencies even though the voltage gain rolls off. The transformer and R3 are used to crank up the input voltage to compensate for the dropping gain. The response is so flat as the ideal op amp model has a single pole rolloff to infinity, an ideal response which can be perfectly compensated over a reasonable range by the transformer circuit. As Russmax noted, real op amps have additional poles and there is usually considerably more phase shift than 90deg at the unity gain frequency.

I have made no effort to make the component values practical and have no idea whether it is possible to do so.

I suspect that practical techniques are limited to the types of peaking caps and chokes shown in earlier posts.

Even if the output impedance is not zero, the power gain will still be infinite because the input impedance is infinite and requires zero power to drive.

In post #68, setting L3 to 87.50 uH, L2 to .125 nH and R3 to .639 ohms gives a bandwidth of about 17 MHz.

We should probably start a new thread to continue this.

Perhaps a moderator could move everything from about post #52 et. seq. to a new thread.

 

Even if the output impedance is not zero, the power gain will still be infinite because the input impedance is infinite and requires zero power to drive.

In post #68, setting L3 to 87.50 uH, L2 to .125 nH and R3 to .639 ohms gives a bandwidth of about 17 MHz.

We should probably start a new thread to continue this.

Perhaps a moderator could move everything from about post #52 et. seq. to a new thread.

It's really not that interesting, the design equations for the non-inverting one are:

\(\omega_0 = 2 \pi F_{GBW}\) is the unity gain frequency of the op amp in radians

\(F_{-3dB}=\frac{1}{2\pi}\sqrt{\frac{\omega_0 R_3}{3L_2}}\) is the new -3dB frequency when

\(L_3=\frac{R_3^2}{9L_2}\left(\frac{3}{\omega_0}+\frac{L_2}{R_3}-\sqrt{\frac{6L_2}{\omega_0 R_3}}\right)^2\)

It's just a trick you can do with the zero output impedance / infinite input impedance of the op amp, but I can't see it's of much use.

 

You confused me, referencing my non-inverting circuit and questioning the limit of inverting circuits.
..................

Mia cuppa.
I didn't notice that your first circuit was also non-inverting.

 

Just to show you how silly it can get, want a sim with 230MHz bandwidth:



There is no limit! (well LTSpice may have some rounding issues at some stage...)

BTW - the transformer has a turns ratio of 158,808:1. Good luck winding that!

 

Your design equation doesn't seem to give the right value for L3 in post #66. You have 21.7uH in the post, but the design equation gives 5.9uH:

You said "LTSpice may have some rounding issues at some stage..."

That's the very issue I think is worth examining for this circuit. The behavior of the circuit is very sensitive to component values for wide bandwidth. I wonder just where LTSpice begins to falter. I'm not getting the same result you do for the 230 MHz wide case. I'm not using LTSpice, but rather I'm just solving the system with the nodal equations. It's possible I haven't got it set up right yet, so I'll look for an error.

Edit: I just realized that L3 in the 230 MHz case is 25.22682 Henries, not microhenries. Now I'm getting better results. You could helped your reader not make this mistake by showing it as 25.22682H, instead of just 25.22682

What are your design equations for the inverting case?

 

Can you publish the model your using?

The model I used, in post 59, is not approaching your model. Your schematic in post 72 barely reaches 200k bandwidth.

I do not use LT Spice.

 

The LTSpice idealized opamp is:

.subckt opamp 1 2 3
G1 0 3 2 1 {Aol}
R3 3 0 1.
C3 3 0 {Aol/GBW/6.28318530717959}
.ends opamp

The two parameters I used in my sims were Aol=1e5 and GBW=1e6

 

The LTSpice idealized opamp is:

.subckt opamp 1 2 3
G1 0 3 2 1 {Aol}
R3 3 0 1.
C3 3 0 {Aol/GBW/6.28318530717959}
.ends opamp

The two parameters I used in my sims were Aol=1e5 and GBW=1e6

Thanks Mike - I hadn't delved into that. My assumption was wrong - this model has a non-zero output impedance: 1Ω || 159nF. My calculations will only be approximately correct for the case when this output impedance is much less than R3.

 

Your design equation doesn't seem to give the right value for L3 in post #66. You have 21.7uH in the post, but the design equation gives 5.9uH:

I initially did a very rough design with a few simplifications, made a few lines of calculation and came up with some rough values. The sim was way off but the design was on the right track and a minute of tweaking gave the ones I posted. Now that Mike has posted the actual op-amp model I can see that the equations I posted won't work so well when the load on the op amp is comparable to it's 1 ohm output impedance. They will work over a wider range if you use an op amp model with a zero output impedance. The sims suggest that the analysis can be changed to cope with the non-zero output impedance but I haven't done that.

You said "LTSpice may have some rounding issues at some stage..."

That's the very issue I think is worth examining for this circuit. The behavior of the circuit is very sensitive to component values for wide bandwidth. I wonder just where LTSpice begins to falter.

I was surprised at the sensitivity to component values, but this is not a numerical issue, but that the flat transfer function is actually a critically damped second order response. It is quite sensitive to the component values to get the critical damping.

What are your design equations for the inverting case?

I only did a rough analysis and tweaked the values in the simulator. An exercise for the interested!

 

Can you publish the model your using?

The model I used, in post 59, is not approaching your model. Your schematic in post 72 barely reaches 200k bandwidth.

I do not use LT Spice.

MikeML posted the model. The critical features are the (impractical) infinite input impedance, the very low output impedance (relative to R3) and a voltage gain around the unity gain frequency and beyond:

\(A_v \approx \frac{\omega_0}{j\omega}\)

 

Hello there,


Sorry, but I could not help but mention that with all of the respondents here not one has mentioned the MOST classic way to increase the bandwidth of an op amp (circa 1970's maybe or earlier). Perhaps you guys should do some hunting on the web

A slightly less issue that also did not come up once yet is the slew rate. Often the slew rate limits the bandwidth too. Given that the input level is known this can also be determined.

I will wait and see if someone can get the good professor to explain his position to the rest of us before commenting more about this

 

I will wait and see if someone can get the good professor to explain his position to the rest of us before commenting more about this

I suspect we will be waiting a very long time before the good professor shows up. I would love to be wrong with that assessment.