SaM - Non-Ideal Operational Amplifier • Input and Output Resistances

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If we consider the Input and Output resisistances non-ideal, we can model an op.amp like this:
So that:$V_{out}^{\prime }=A_d{V}_d+A_c{V}_c$Where:

• $V_d=V_2-V_1$ (so the voltage on $R_D$)
• $V_C=\frac{V_2+V_1}{2}$ (so the voltage on $R_{C1}$ plus the voltage on $R_{C2}$)
• $A_d=\frac{A_2-A_1}{2}$
• $A_C=A_2+A_1$
  • $A_1={V_{out}|}_{V_2=0}$
  • $A_2={V_{out}|}_{V_1=0}$
• $R_{C1}$ and $R_{C2}$ are the “common mode resistances”. (Ideally they are both $\infty$NOT_SURE_ABOUT_THIS )
• $R_D$ is the “differential mode resisitance”. (Ideally we consider it $\infty$)
• $R_0$ is the “output resistance, ideally it’s $0$.
• ==Normally, an ideal op.amp. would have only $A_d=A=\infty$ for the output, however in reality, the ouput also depends on $A_c{V}_c$==.

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We can imagine it a connected to a resistive bridge, and here is a somewhat thevenim equivalent

• $R_{TH}^{\prime }=R_1\parallel R_4$.
• $R_{TH}=R_2\parallel R_3$. (This can also be a sensor, if we use a half or full bridge)
• $V_{CC}=V\frac{R_2}{R_2+R_3}$ “offset voltage”.
• $V_{TH}=V\left(\frac{R_1}{R_1+R_4}-\frac{R_2}{R_2+R_3}\right)$ is the”changing part” given by our sensor.
• Using this model we don’t lose the $V^{+}$ and $V^{-}$ nodes that connect the bridge to the amplifer.

The actual thevenim equivalent would have been:

• $V_{TH}=V\left(\frac{R_1}{R_1+R_4}-\frac{R_2}{R_2+R_3}\right)$
• $R_{TH}=(R_1\parallel R_4)+(R_2\parallel R_3)$
• Source: Youtube.

So finally if we unite the two circuits:

• $R_C\gg R_{TH}$
• We have that the output will be (we consider a balanced bridge):$V_{out}^{\prime }=A_d{V}_d+A_c\left(V_{CC}+\frac{V_d}{2}\right)$NOT_SURE_ABOUT_THIS (How the fuck was this result found???), mentioned in: Lecture 11_03, Lecture 12_02, Lecture 12_03
• What are some common values for differencial input resistance, common input resistance, and output resistance, of an operational amplifier? (ChatGPT)
  • The input and output resistances of an operational amplifier (op-amp) can vary depending on the specific model and manufacturer.
    However, I can provide you with some typical values that you might encounter in general:
  1. Differential Input Resistance ($R_{in}$​):
     Commonly in the range: $\left[10^5\text{ohm}÷10^{14}\text{ohm}\right]$.
  2. Common Input Resistance ($R_c$​):
     Commonly in the range: $\left[10^9\text{ohm}÷10^{12}\text{ohm}\right]$.
  3. Output Resistance ($R_0$​):
     Generally low: $<100\text{ohm}$.
  • Remember, these are rough values, and actual specifications can vary.
    Always refer to the datasheet of the specific operational amplifier you are working with for precise information.
    If you have a particular op-amp in mind, I can provide more specific details using the mathjax format you specified.