Open Loop Gain of Amplifier

[FAS1998]

Homework Statement

An amplifier has an open-loop gain of A and two poles at 10 MHz and 500 MHz. Calculate A for a phase margin of 60◦

Relevant Equations

Open Loop Gain = -A(s)F(s)
Phase Margin = <F(jwo)A(jwo)

I’m totally lost and struggling to understand my lecture notes. Can somebody point me in the right direction?

 

[ammarb32]

Do you have any other information like a diagram or anything else? You mentioned the two poles at 10 MHz and 500 MHz. I would suggest you start off by finding a relationship (or a "function") that relates the output versus your input? It's a specific type of function, you might've already covered it in your classes.

 

[DaveE]

I think we need to know where those poles are in relation to the feedback network, also what is the amount (i.e. DC gain) of the feedback network.

Step 1 - Draw a schematic or signal block diagram and post it.

 

[FAS1998]

I think we need to know where those poles are in relation to the feedback network, also what is the amount (i.e. DC gain) of the feedback network.

Step 1 - Draw a schematic or signal block diagram and post it.

This is the entire question as written in my assignment. I’m not sure what else I can include.

 

[Twigg]

If I'm understanding the problem correctly, the feedback loop is a short-circuit (inverting follower aka inverting buffer amplifier).

You have two unknowns, the open-circuit gain and the frequency at which a phase margin of $60^{\circ}$ occurs. What does the $60^{\circ}$ phase margin tell you about the relationship of the input and output voltages?

 

[FAS1998]

If I'm understanding the problem correctly, the feedback loop is a short-circuit (inverting follower aka inverting buffer amplifier).

You have two unknowns, the open-circuit gain and the frequency at which a phase margin of $60^{\circ}$ occurs. What does the $60^{\circ}$ phase margin tell you about the relationship of the input and output voltages?

That there is a phase angle of 60 - 180 = -120 degrees?

 

[Twigg]

How would you write this as a ratio, $\frac{V_{out}}{V_{in}}$? Remember that the phase margin occurs at 0dB.

Can you write a another algebraic equation for $V_{out}$ and $V_{in}$ in terms of $A_{OL}$ and the poles? It will help to draw out the block diagram here.

 

[DaveE]

This is the entire question as written in my assignment. I’m not sure what else I can include.

OK, then we can guess at a reasonable model.

Phase margin is used in the context of feedback loop stability, so the inputs and outputs are irrelevant. It is the loop gain that you care about. It only makes sense that those poles must appear in the loop gain, or they would also be irrelevant. Let's assume that the only gain in the system is the amplifier A, with unity gain feedback.

So, let's say you have and amplifier with gain A and poles at 10MHz and 500MHz, then you apply unity gain negative feedback. Can you write an equation (vs. frequency) for the total loop gain (the gain a signal sees as it travels through the amplifier and the feedback path back to it's original starting point)?

Can you describe what phase margin is and apply a constraint to that loop gain equation.

 

[Twigg]

In hindsight I realize introducing inputs and outputs was needlessly confusing. Sorry about that. What @DaveE is saying leads to the same solution I worked out.