ENSC2003 - Lecture 9

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ENSC2003 - Lecture 8
Operational Amplifiers - Slides

Operational Amplifiers

• Operational amplifiers are used to amplify voltage
  • Also known as op-amp and difference amplifiers
  • Op-amps are non-linear elements
• Used to perform mathematical operations

• Two input terminals:
  • $+$ -> noninverting terminal
  • $-$ -> inverting terminal
• $V_{out}$ $-$ output voltage at the output terminal
  • Should be much larger than input voltage
• $V_{S+}$ and $V_{S-}$ $-$ Power supply terminals

KCL of an op-amp:
$I_{+}+I_{-}+I_{S+}+I_{S-}+I_o=0$

Equivalent Circuit Model

• Equivalent circuit model of an op-amp:

  
  $V_{S+}$ and $V_{S-}$ are ignored, but the op-amp must be connected to a DC power supply to work

• This is a more practical but more complicated model

$V_i$ is the differential input voltage:
$V_i=V_{+}-V_{-}$
$R_i$ is the input resistance of the device
$R_o$ is the output resistance of the device

$A$ is the open loop gain -> gain of op-amp with no feedback connection applied in circuit

• Extremely high for most practical op-amps ($A\to \infty$)

$V_o=A(V_{+}-V_{-})$

• Linear region: $V_o$ changes linearly with respect to $V_i$
  • Perfect op-amp should only be working in the linear region
• Saturation region: output voltage is limited by power supplies it is connected to → saturates at power supply voltage
  i.e. op-amp cannot generate an output voltage that is higher than positive supply $V_{S+}$ or lower than negative supply $V_{S-}$

Ideal Op-Amp Model & Golden Rules

• Ideal → easier model

  

• An ideal op-amp is an amplifier with infinite open-loop gain, infinite input resistance, and zero output resistance

  • Infinite open-loop gain, $A\to \infty$
  • Infinite input resistance, $R_i\to \infty$
  • Zero output resistance, $R_o\approx 0$

• $ These assumptions lead to what is known as Golden Rules:
  $I_{+}=I_{-}=0A$
  $V_{+}-V_{-}=0V\to V_{+}=V_{-}$
  These equations are only true for the ideal model

Applications of Ideal Op-Amp

• Two ways to connect op-amp to circuit:
  • Open loop
  • Closed loop

Open Loop $-$ no circuit loops that connect output to any input

• Open-loop configuration is not practical because the very high gain of the op-amp creates poor stability

  • Never used

  

Closed Loop $-$ one or more circuit loops connect output to inputs

• We will use this configuration

  

Closed loop gain $A_{ct}$ of the circuit:
$A_{ct}=\frac{V_o}{V_i}=1+\frac{R_f}{R_1}$
$V_o$ $-$ output voltage
$V_i=V_{+}-V_{-}$

• You can control output voltage through your resistors:
  • If $R_f=0$ -> short circuit, then $V_o=V_i$
  • If $R_1\to \infty$ -> open circuit, then $V_o\approx V_i$

Closed loop circuits either negative or positive feedback configuration

• Positive feedback -> $V_o$ routed back to noninverting $(+)$ terminal

  

  • Input and output voltage have same sign

• Negative feedback -> $V_o$ routed back to inverting $(-)$ terminal

  

  • Input and output voltage have different sign

The only methodologies we use to solve any op-amp question are NTD and the Golden Rules, however, you must never write KCL equations for the output node of the op-amp

• ! Current the flows into the op-amp is either $i_{+}$ or $i_{-}$ $\Rightarrow 0$

Weighted Summing Amplifier

• Weighted summing amplifier is an op-amp circuit with multiple input voltages where $V_o$ is the weighted sum of the inputs

  

Voltage out for inverting weighted summer:
$V_o=-(\frac{R_f}{R_1}{V}_1+\frac{R_f}{R_2}{V}_2+\cdots +\frac{R_f}{R_n}{V}_n)$

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ENSC2003 - Lecture 10