93 lines
3.0 KiB
Markdown
93 lines
3.0 KiB
Markdown
![[op-amp-basic-schematic-symbol.svg]]
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The operational amplifier has a very high input impedance which makes it very good for amplifying low voltage signals.
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Basically the OpAmp is a function like this:
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$\displaystyle Y = A_v (X_1 - X_2)$
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Where:
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$$
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\begin{flalign}
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&Y = \text{Output Voltage}&\\\
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&A_v = \text{Open Loop Gain}\\
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&X_1 = \text{Input V1 (Non Inverting Input)}\\
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&X_2 = \text{Input V2 (Inverting Input)}\\
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\end{flalign}
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$$
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# Rules
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**1. No Current flows in or out of the outputs**
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**2. The op-amp tries to keep the input voltages the same**
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The second rule only applies when the op-amp is in closed loop configuration
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# Regions
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Op Amps functions in different regions, just like diodes, and transistors.
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![[op-amp-regions.png|400]]
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# Regions
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**Linear Region**
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This is how the Op-Amp normally functions.
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**Saturation Region**
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When the output of the op-amp would be higher than $+V_{CC}$ or lower than $-V_{CC}$ the output value is clamped to those values.
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In real life OpAmps have $A_V$ values as high as $10^8$ or $10^9$ due to this even very small input voltages would quickly leave the linear region. That is why we need
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# Negative Feedback
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To use negative feedback we connect the output of the OpAmp to one of its inputs. This connection is modified by a *feedback factor* ($\beta$) which can be in the range $0 \le \beta \le 1$.
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Due to this feedback the new formula for the output $V_O$ is now:
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$$
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\begin{flalign}
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&V_o = A_V * V_\Delta&\\\
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\\
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&V_- = \beta * V_o\\
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&\text{Now we can say that }V_\Delta \text{is equal to:}\\
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&V_\Delta = V_+ - \beta *V_o &| \textit{ Solve for }V_o \\
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&V_o = \frac{V_+ - V_\Delta}{\beta}
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\end{flalign}
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$$
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# Configurations
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**Open Loop**
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When the output of the Op Amp is not connected to any of its inputs, it is in the so called "open loop configurations"
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**Closed Loop**
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When we connect the output of the OpAmp to either $V_+$ or $V_-$ the OpAmp is in the "closed loop configuration".
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# Bandwidth Limitations
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Real op-amps behave differently depending on the input signals frequency. Usually the internal open-loop gain gets lower as the input frequency gets higher like this.
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The op-amps bandwidth is the frequency range in which the voltage gain is above 70.7% ($3dB$) of its maximum output. The point at which it is below that gain, is called the **breakpoint**.
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![[op-amp-bandwidth.png|400]]
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This is also one of the reason we use op-amps in closed loop configuration. Because it allows is to trade maximum gain for a larger bandwidth.
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![[op-amp-bandwidth-closed-loop.png|400]]
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If we want to find out the bandwidth of an op-amp, we can check the datasheet. The *LM741 OpAmp* for example:
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![[lm741-datasheet-bandwidth.png]]
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The thing is that this frequency only applies when the op-amp has a gain of 1, this frequency point is also called **unity gain**. It is called the **Gain Bandwidth Product**, which is calculated as follows:
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$GBP = A_V * f_c$
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Where $A_V$ is the voltage gain, and $f_c$ is the cutoff frequency.
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With this equation we can also solve for $f_c$ like so:
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$\displaystyle f_c = \frac{GBP}{A_V}$
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![[lm741.pdf]] |