How can I find the open loop voltage gain of this opamp?

• Engineering
• Boltzman Oscillation
In summary, the conversation discusses how to find the open-loop voltage gain for a given op amp model, which is represented by the equation u(s) = u_o / (1 + s/w_o). The speaker suggests using a non-ideal op amp model and analyzing the circuit to find the transfer function Vo/Vin, which will have a denominator term of the form (1 + s/w_o) to determine the bandwidth of the circuit. The conversation also touches upon the use of inductors and capacitors in the frequency domain and the relationship between gain and bandwidth.
Boltzman Oscillation
Homework Statement
Given a non-ideal op amp model, find the open loop voltage gain in the given format.
Relevant Equations
Below
The open loop voltage gain is given as :
$$u(s) = \frac{u_o}{1+\frac{s}{w_o}} = \frac{100}{1 + \frac{s}{40}}$$
Where u_o is the d.c. voltage gain and w_o is the pole.
The op amp that is given is:

And I am told to use the non ideal op amp model as follows:
Well my guess is that I can find the D.C voltage gain by substituting this model into the circuit shown in figure 1. I would not remove the feedback in order to find the D.C. voltage gain. If i find the voltage across r_o and then using it in the following formula:
$$u_o = \frac{V_{in}}{V_{out}} = \frac{V_{ro}}{V_{out}}$$

then i should be able to plug this into the equation for u(s) but then I would be missing the value for w_o. Am I thinking this correctly? What am I doing wrong or in what direction should I take this?

So you want to find the "open-loop voltage gain" ...which is then written down by you in the next line...?
Sounds a bit confusing...

Draw the resistor network in Fig 15a, but without the op-amp. Between Rs and R1 add the 1k resistor, and feeding the junction of R2 and RL add the 500Ω resistor, and to the free end of that 500Ω draw a voltage-controlled voltage source, A.vΔ. Now analyse that circuit to derive the transfer function, Vo/Vin. There will be a denominator term of the form (1 + s/ωf) to tell you the bandwidth of that circuit with a finite-gain amplifier.

LvW said:
So you want to find the "open-loop voltage gain" ...which is then written down by you in the next line...?
Sounds a bit confusing...
Sorry I am trying to derive it.

NascentOxygen said:
Draw the resistor network in Fig 15a, but without the op-amp. Between Rs and R1 add the 1k resistor, and feeding the junction of R2 and RL add the 500Ω resistor, and to the free end of that 500Ω draw a voltage-controlled voltage source, A.vΔ. Now analyse that circuit to derive the transfer function, Vo/Vin. There will be a denominator term of the form (1 + s/ωf) to tell you the bandwidth of that circuit with a finite-gain amplifier.
Alright I will try this method but I do have one concern: usually inductors and capacitors have the s variable when they are transformed into the frequency domain, where will I get the s variable here?

Boltzman Oscillation said:
Alright I will try this method but I do have one concern: usually inductors and capacitors have the s variable when they are transformed into the frequency domain, where will I get the s variable here?
The only component in the given circuit with an "s" in its relationship is the first-order falloff characteristic of the op-amp, μ(s).

BTW, I assume you are wanting to find the closed-loop response of this amplifier?

Boltzman Oscillation said:
Sorry I am trying to derive it.

...to derive it... WHAT do you want to derive?
Please try to formulate a clear question .

For my opinion, only two alternatives do exist:

1) What is the closed-loop gain when an open-loop gain expression is given?
2.) What is the open-loop gain when an equivalent circuit diagram is given?

So - what do you need?

BvU
NascentOxygen said:
The only component in the given circuit with an "s" in its relationship is the first-order falloff characteristic of the op-amp, μ(s).

BTW, I assume you are wanting to find the closed-loop response of this amplifier?
Well I am given the open loop voltage gain which I show as the first equation. I want to find out how they got that.

Boltzman Oscillation said:
Well I am given the open loop voltage gain which I show as the first equation. I want to find out how they got that.
I would think they constructed an amplifier on a silicon chip, then measured its output versus input for sinusoids and approximated that plot to a first-order system.

The wording in the instructions doesn't seem right, that's why I'm talking about finding closed loop response when told the open-loop response. It would be a good idea to check exactly what the task is that you have been set.

Has over 2 000 000 hits. Looks like the stuff you are after is in the first few on the first page.

For the bandwidth, or location of the first pole, recall that the gain_bandwidth product is a constant for any given amplifier. So if you know the bandwidth and one gain value, the bandwidth at other gains is inversely proportional to the relative gains.

Cheers,
Tom

1. What is an opamp and why is the open loop voltage gain important?

An opamp, short for operational amplifier, is an electronic device used to amplify a signal. The open loop voltage gain is the ratio of the output voltage to the input voltage when there is no feedback in the circuit. It is important because it determines the amplification capability and stability of the opamp.

2. How can I measure the open loop voltage gain of an opamp?

The open loop voltage gain can be measured by applying a known input voltage and measuring the output voltage. The gain can then be calculated by dividing the output voltage by the input voltage. This process should be repeated for different input voltages to determine the gain at different levels.

3. What factors affect the open loop voltage gain of an opamp?

The open loop voltage gain of an opamp can be affected by factors such as temperature, power supply voltage, and component tolerances. In addition, the frequency of the input signal can also have an impact on the gain, as opamps have a limited bandwidth.

4. Can the open loop voltage gain of an opamp be modified?

Yes, the open loop voltage gain of an opamp can be modified by adding external components such as resistors and capacitors in a feedback configuration. This is known as closed loop operation and allows for more precise control of the amplification of the opamp.

5. Are there any standard values for the open loop voltage gain of an opamp?

No, there are no standard values for the open loop voltage gain of an opamp as it can vary depending on the specific opamp model and manufacturer. However, most opamps have a typical gain range of 10,000 to 100,000, with some specialized opamps having gains in the millions.

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