## viernes, 29 de enero de 2010

### Operational amplifier applications

This article illustrates some typical applications of operational amplifiers. A simplified schematic notation is used, and the reader is reminded that many details such as device selection and power supply connections are not shown.

Linear circuit applications

Comparator:

Comparator
Compares two voltages and switches its output to indicate which voltage is larger.

• $V_{\text{out}} = \left\{\begin{matrix} V_{\text{S+}} & V_1> V_2 \\ V_{\text{S-}} & V_1 < V_2 \end{matrix}\right.$
(where Vs is the supply voltage and the opamp is powered by + Vs and Vs.)

### Inverting amplifier:

Inverting amplifier
An inverting amplifier uses negative feedback to invert and amplify a voltage. The Rf resistor allows some of the output signal to be returned to the input. Since the output is 180° out of phase, this amount is effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is dubbed negative feedback.
$V_{\text{out}} = -\frac{R_{\text{f}}}{R_{\text{in}}} V_{\text{in}}\!\$

• Zin = Rin (because V is a virtual ground)

• A third resistor, of value $R_{\text{f}} \| R_{\text{in}} \triangleq R_{\text{f}} R_{\text{in}} / (R_{\text{f}} + R_{\text{in}})$, added between the non-inverting input and ground, while not necessary, minimizes errors due to input bias currents.

The gain of the amplifier is determined by the ratio of Rf to Rin. That is:
$A = -\frac{R_f}{R_{in}}$
The presence of the negative sign is a convention indicating that the output is inverted. For example, if Rf is 10,000 Ω and Rin is 1,000 Ω, then the gain would be -10000Ω/1000Ω, which is -10.

### Non-inverting amplifier:

Non-inverting amplifier
Amplifies a voltage (multiplies by a constant greater than 1)
$V_{\text{out}} = V_{\text{in}} \left( 1 + \frac{R_2}{R_1} \right)\,$

• Input impedance $Z_{\text{in}} \approx \infin$

• The input impedance is at least the impedance between non-inverting ( + ) and inverting ( ) inputs, which is typically 1 MΩ to 10 TΩ, plus the impedance of the path from the inverting ( ) input to ground (i.e., R1 in parallel with R2).

• Because negative feedback ensures that the non-inverting and inverting inputs match, the input impedance is actually much higher.

• A resistor of value

$R_1 \| R_2 \triangleq \left(\frac{1}{R_1} + \frac{1}{R_2}\right)^{-1} = \frac{ R_1 R_2 }{ R_1 + R_2 },\,$
• which is the equivalent resistance of R1 in parallel with R2, between the Vin source and the non-inverting ( + ) input will ensure the impedances looking out of each input will be matched.

Differential amplifier:

Differential amplifier
The circuit shown is used for finding the difference of two voltages each multiplied by some constant (determined by the resistors).
The name "differential amplifier" should not be confused with the "differentiator", also shown on this page.
$V_{\text{out}} = \frac{ \left( R_{\text{f}} + R_1 \right) R_{\text{g}} }{\left( R_{\text{g}} + R_2 \right) R_1} V_2 - \frac{R_{\text{f}}}{R_1} V_1$

• Differential Zin (between the two input pins) = R1 + R2 (Note: this is approximate) Differential amplifier

Voltage follower:

Voltage follower
Used as a buffer amplifier to eliminate loading effects (e.g., connecting a device with a high source impedance to a device with a low input impedance).
$V_{\text{out}} = V_{\text{in}} \!\$
$Z_{\text{in}} = \infty$ (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)
Due to the strong (i.e., unity gain) feedback and certain non-ideal characteristics of real operational amplifiers, this feedback system is prone to have poor stability margins. Consequently, the system may be unstable when connected to sufficiently capacitive loads. In these cases, a lag compensation network (e.g., connecting the load to the voltage follower through a resistor) can be used to restore stability. The manufacturer data sheet for the operational amplifier may provide guidance for the selection of components in external compensation networks. Alternatively, another operational amplifier can be chosen that has more appropriate internal compensation.

### Summing amplifier:

Summing amplifier

A summing amplifer sums several (weighted) voltages:
$V_{\text{out}} = -R_{\text{f}} \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \cdots + \frac{V_n}{R_n} \right)$

• When $R_1 = R_2 = \cdots = R_n$, and Rf independent
$V_{\text{out}} = -\frac{R_{\text{f}}}{R_1} ( V_1 + V_2 + \cdots + V_n ) \!\$

• When $R_1 = R_2 = \cdots = R_n = R_{\text{f}}$
$V_{\text{out}} = -( V_1 + V_2 + \cdots + V_n ) \!\$

• Output is inverted

• Input impedance of the nth input is Zn = Rn (V is a virtual ground)

### Integrator:

Integrating amplifier

Integrates the (inverted) signal over time
$V_{\text{out}} = -\int_0^t \frac{ V_{\text{in}} }{RC} \, \operatorname{d}t + V_{\text{initial}}\,$
(where Vin and Vout are functions of time, Vinitial is the output voltage of the integrator at time t = 0.)

• Note that this can also be viewed as a low-pass electronic filter. It is a filter with a single pole at DC (i.e., where ω = 0) and gain.

• There are several potential problems with this circuit.

• It is usually assumed that the input Vin has zero DC component (i.e., has a zero average value). Otherwise, unless the capacitor is periodically discharged, the output will drift outside of the operational amplifier's operating range.

• Even when Vin has no offset, the leakage or bias currents into the operational amplifier inputs can add an unexpected offset voltage to Vin that causes the output to drift. Balancing input currents and replacing the non-inverting ( + ) short-circuit to ground with a resistor with resistance R can reduce the severity of this problem.

• Because this circuit provides no DC feedback (i.e., the capacitor appears like an open circuit to signals with ω = 0), the offset of the output may not agree with expectations (i.e., Vinitial may be out of the designer's control with the present circuit).
Many of these problems can be made less severe by adding a large resistor RF in parallel with the feedback capacitor. At significantly high frequencies, this resistor will have negligible effect. However, at low frequencies where there are drift and offset problems, the resistor provides the necessary feedback to hold the output steady at the correct value. In effect, this resistor reduces the DC gain of the "integrator" – it goes from infinite to some finite value RF / R.

### Differentiator:

Differentiating amplifier

Differentiates the (inverted) signal over time.
The name "differentiator" should not be confused with the "differential amplifier," which is also shown on this page. The former takes a derivative and the latter takes a difference (i.e., does subtraction). This is a circuit that could be used in an analog computer, but in practice these circuits are difficult to keep stable and noise-free, so often the problem can be rearranged to use an integrator instead.
$V_{\text{out}} = -RC \,\frac{\operatorname{d}V_{\text{in}} }{ \operatorname{d}t} \, \qquad \text{where } V_{\text{in}}\text{ and } V_{\text{out}} \text{ are functions of time.}$

### Instrumentation amplifier:

Instrumentation amplifier
Combines very high input impedance, high common-mode rejection, low DC offset, and other properties used in making very accurate, low-noise measurements

### Schmitt trigger:

Schmitt trigger with non-inverting hysteretic switching characteristic
In this configuration, the hysteresis curve is non-inverting (i.e., very negative inputs correspond to a negative output and very positive inputs correspond to a positive output), and the switching thresholds are $\pm \frac{R_1}{R_2}V_{\text{sat}}$ where Vsat is the greatest output magnitude of the operational amplifier.

Schmitt trigger with inverting hysteretic switching characteristic
Alternatively, the input and the ground may be swapped. In this configuration, the hysteresis curve is inverting (i.e., very negative inputs correspond to a positive output and vice versa), and the switching thresholds are $\pm \frac{R_1}{R_1 + R_2} V_{\text{sat}}$. Such a configuration is used in the relaxation oscillator shown below.

### Relaxation oscillator:

Relaxation oscillator implemented with inverting Schmitt trigger and RC network
By using an RC network to add slow negative feedback to the inverting Schmitt trigger, a relaxation oscillator is formed. The feedback through the RC network causes the Schmitt trigger output to oscillate in an endless symmetric square wave (i.e., the Schmitt trigger in this configuration is an astable multivibrator).

### Inductance gyrator:

Inductance gyrator

Simulates an inductor (i.e., provides inductance without the use of an possibly costly inductor).

DAHIANA ALEJANDRA ROSALES HERNÁNDEZ

EES

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## jueves, 28 de enero de 2010

### Single-ended and differential amplifiers

For ease of drawing complex circuit diagrams, electronic amplifiers are often symbolized by a simple triangle shape, where the internal components are not individually represented. This symbology is very handy for cases where an amplifier's construction is irrelevant to the greater function of the overall circuit, and it is worthy of familiarization:

The +V and -V connections denote the positive and negative sides of the DC power supply, respectively. The input and output voltage connections are shown as single conductors, because it is assumed that all signal voltages are referenced to a common connection in the circuit called ground. Often (but not always!), one pole of the DC power supply, either positive or negative, is that ground reference point. A practical amplifier circuit (showing the input voltage source, load resistance, and power supply) might look like this:
Without having to analyze the actual transistor design of the amplifier, you can readily discern the whole circuit's function: to take an input signal (Vin), amplify it, and drive a load resistance (Rload). To complete the above schematic, it would be good to specify the gains of that amplifier (AV, AI, AP) and the Q (bias) point for any needed mathematical analysis.

If it is necessary for an amplifier to be able to output true AC voltage (reversing polarity) to the load, a split DC power supply may be used, whereby the ground point is electrically "centered" between +V and -V. Sometimes the split power supply configuration is referred to as a dual power supply.
The amplifier is still being supplied with 30 volts overall, but with the split voltage DC power supply, the output voltage across the load resistor can now swing from a theoretical maximum of +15 volts to -15 volts, instead of +30 volts to 0 volts. This is an easy way to get true alternating current (AC) output from an amplifier without resorting to capacitive or inductive (transformer) coupling on the output. The peak-to-peak amplitude of this amplifier's output between cutoff and saturation remains unchanged.

By signifying a transistor amplifier within a larger circuit with a triangle symbol, we ease the task of studying and analyzing more complex amplifiers and circuits. One of these more complex amplifier types that we'll be studying is called the differential amplifier. Unlike normal amplifiers, which amplify a single input signal (often called single-ended amplifiers), differential amplifiers amplify the voltage difference between two input signals. Using the simplified triangle amplifier symbol, a differential amplifier looks like this:
The two input leads can be seen on the left-hand side of the triangular amplifier symbol, the output lead on the right-hand side, and the +V and -V power supply leads on top and bottom. As with the other example, all voltages are referenced to the circuit's ground point. Notice that one input lead is marked with a (-) and the other is marked with a (+). Because a differential amplifier amplifies the difference in voltage between the two inputs, each input influences the output voltage in opposite ways.

DAHIANA ALEJANDRA ROSALES HERNÁNDEZ
EES