SaM - Non-Ideal Operational Amplifier • OZE (Out of Zero Error) • Special Kinds of Operational Amplifiers • Precision Amplifier • Low Noise • Low Input Bias Current • Zero Drift • Low Noise Operational Amplifier

In an operational amplifier we need to consider an input offset $\left(V_{io}\right)$ and two bias currents $\left(I_{b1},I_{b2}\right)$, we can model it like this:

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We can then model the whole measurement system, by adding the Thevenim equivalent of the measurement system as the input to the amplifier:

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If we wish to know the effect of the non-idealities of the amplifier on the output we can calculate ${V_{out}|}_{V_s=0}$ and the result is:IMPORTANTE ${V_{out}|}_{V_s=0}=\left(1+\frac{R_2}{R_1}\right)\left(I_{b2}{R}_S-I_{b1}\frac{R_1{R}_2}{R_1+R_2}+V_{io}\right)$And this is called OZE: Out of Zero Error.

While we can also define the IZE: Input out of Zero Error:$\text{IZE}=I_{b2}{R}_S-I_{b1}\frac{R_1{R}_2}{R_1+R_2}+V_{io}$Even if the source $V_S=0$, since the amplifier is not ideal, we will measure an ouput like if $V_S=\text{IZE}$ and an having ideal operational amplifier.

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By having an OZE we have a non-symmetrical dynamic range:
Ideally we want no OZE and a $0\text{V}$ output if the input is $0\text{V}$. Instead we have $V_{out}=\text{OZE}$ for $V_S=0\text{V}$. ==However if the OZE is constant, this is not a big problem, since it can be corrected==.

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The real problem is that the OZE is not constant, instead it has a drift, due to envirement condition, aging, temperature, …, and this variation cannot be corrected :
(green/blue line: real OZE) (red line : previously calculated OZE)

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For this reason, if we want a high accuracy we need to select a special kind of amplifier, called ==“precision amplifier”==. These devices are often low freqeuncy device (or “narrow bandwidth devices”, it means the same thing), but with really low DC errors.

We can find different classes of precision amplifeirs:IMPORTANTE

1. Low input bias current op. amp. with $I_b<100\text{pA}$.
2. Precision amplifiers with $V_{io}<1\text{mV}$ (can also be found with $V_{io}$ in the range of $\sim \mu \text{V}$) and with a $\text{TCV}<2\frac{\mu \text{V}}{°\text{C}}$ (Temperature Coefficicent of Voltage, similar to the TCR).
3. Zero drift op. amp. $V_{io}\sim 5\mu \text{V}$, $\text{TCV}<2\frac{\text{nV}}{°\text{C}}$, however these are slow devices, so a high rise time (or “limited slew rate”) and also have a really narrow band.
4. Low noise amplifier: they minimize the white noise interferance and not the DC offset.
   Here’s how we can model the input-noise in an amplifier:
   

Here’s a table to better rember them:

	$I_b$	$V_{io}$	TCV	Other
Low input bias current op.amp.	$<100\text{pA}$
Precision amplifiers		$<1\text{mV}$	$<2\frac{\mu \text{V}}{°\text{C}}$
Zero drift op. amp		$\sim 1000$ times lower then precision amplifiers	$\sim 1000$ times lower then precision amplifiers	Slow devices (high rise time)
Low noise amplifier				Minimize the white noise interferance.

As a rule of thumb we can also say that generarly the drift offset can be considered equal to: IMPORTANTE $$V_{\small{\text{DRIFT}}} = {1 \over 10} V_{io}$$$V_{io}$ (the input offset of the amplifer) is given by the manifacturer in the data-sheet.

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So to summarize for DC measurement we have that:IMPORTANTE

• DC offset: can be corrected
• Drift offset (variable offset): cannot be corrected.
• $V_{\text{DRIFT}}=\frac{1}{10}{V}_{io}$.

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Memory Card

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