 # Basic operational amplifier (OpAmp) circuits

22 Nov 2020 - tsp
Last update 30 Oct 2021 12 mins

Since I’m currently working again with OpAmp circuits - although in a little bit different setting than the circuits that are described below, I thought it would be a good idea to write a short summary about the most basic circuits and some basic characteristics of OpAmps:

A follow-up blog post will look into some more advanced usages of OpAmps like

• Integrator
• Differentiator
• Peak detector
• Negative resistance circuits

I’ve also written a short lists of OpAmps that I’m usually using for various projects as a quick reference by myself.

Please note: This blog post only discusses voltage feedback OpAmps, i.e. OpAmps with voltage outputs and voltage inputs. There are different classes of OpAmps that provide current feedback, current sources and current sinks (sometimes even mixed). Refer to the specific datasheets in this cases. A voltage sink has a high input impedance, a current sink a low input impedance. These amplifiers are then called trans conductance amplifier, trans impedance amplifier or current amplifier (depending on the feedback network they can be realized with a generic standard OpAmp though).

As usual: Read the datasheets carefully. Operational amplifiers are not exchangeable generally - one has to use amplifiers selected specifically for the given problem

## What is an operational amplifier - anyways? Basically an operational amplifier is a class of a differential amplifier. In it’s ideal configuration it’s an amplifier with two inputs that amplifies the sum between those two inputs. To achieve this one of the inputs is configured as inverted input, so in fact it amplifies the difference between these two inputs:

[ U_{Out} = G * (U_{non inverted} - U_{inverted}) ]

In it’s ideal configuration the amplifier has zero leakage current so no current is flowing into the terminals. As it turns out this approximation fits many applications and depending on the used amplifier the input impedance can be anywhere from a few $k\Omega$ up to many $T\Omega$ which can be seen as $\infty$ in many applications. For applications that require high input impedance and/or work with low currents (it’s reasonable to work with pico and femto amperes with specialized OpAmps) this might require additional considerations. For the ideal OpAmp thou one can assume that

[ R_{in} \to \infty ]

The second ideal property assumed during idealized calculations is an infinite gain factor $G$:

[ G \to \infty ]

Of course this is also not possible in reality. First off an OpAmp cannot output voltages outside it’s input voltage boundaries. So the amplified signal is also clamped to these boundaries - one would then say it has driven the signal into saturation.

On the other hand amplification can be large but never infinite - the open loop gain of many amplifiers is pretty huge (up to $G=3000$ or $G=10000$). Note that one cannot really use most amplifiers in an open configuration in an sane way though - one really has to read the datasheets for which gains these amplifiers are designed. The real gain will then be determined by the feedback network configuration that will also determine the behavior of the amplifier itself - which the remaining page will be about. Note that only a special class of amplifiers is capable of providing stable unity gain ($G=1$) and only a really small subset is capable of being used in open gain configurations. Read the datasheets.

### Power decoupling

Usually operational amplifiers require power supply decoupling. This is not shown in the configurations discussed below but it’s a crucial part of stable operation. The standard decoupling network that works most of the time consists of a metal film capacitors in the range of a few $0.1 \mu F$ down to $pF$ (depending on the frequencies in use) and parallel electrolytic capacitors in the range of $30 \mu F$ as close to the operational amplifier as possible - and separated from the signal traces on the other hand.

### Gain bandwidth product

This is another crucial parameter that’s forgotten often by beginners. The gain bandwidth product is exactly what it sounds like - the result of multiplying the selected configured gain (by the feedback network) with the bandwidth of the signal that should be amplified:

[ GBWP = BW * G ]

There usually is a limitation on the achievable gain at a given bandwidth - the higher the gain the lower the bandwidth. Datasheets usually contain a fixed number as well as a graph describing this relation. Be sure to check these graphs in the datasheet while selecting your OpAmps.

### DC decoupling and impedance matching

Depending on your signal it might be required to provide DC decoupling - this is usually done by a really small capacitor (for example $1 pF$) that’s used in series to the OpAmps input inside the signal path - or even only a coupled transmission line when using microstrip configurations.

Impedance matching gets rather important for higher frequencies - one has to match the sink to the source resistance to fulfill the power transfer theorem (in fact one has to decide if one’s designing for optimal power transfer in which case the sink impedance is the complex conjugate of the source resistance ($Z_{source} = Z_{sink}^*$)) or if one wants to have reflection-less matching which is the case for most high frequency applications except antennas - in which case the source resistance has to match the sink resistance ($Z_{source} = Z_{sink}$).

The most basic network to provide impedance matching is a simple Pi-Type matching network - but these won’t be handled by this blog post anyways.

## Voltage follower, Buffer amplifier

The most basic OpAmp circuit that’s possible. It’s purpose is to provide a high impedance input (depending on the OpAmp between a few Kilo- to multiple Terra-Ohms) and a low impedance output - one can also call this a buffer amplifier. It can be used in many applications:

• Allowing an ADC to measure a voltage from a high impedance / low current capable source.
• Providing a low loss reference voltage when a diode is used as voltage reference.
• As a regulate able power source when the inputs are driven via a DAC which allows easy digital controllable signal generators and lab power supplies up to a few amperes of current (in fact I’ve used an OPA549 OpAmp that way - this OpAmp even supports current limiting and is built exactly for this kind of operation). To build an OpAmp in voltage follower configuration just feed back the output pin to the inverting input pin. The input signal is attached to the non inverting input. Since there is in the ideal case no current flowing through the input pins no current is flowing through the input pins ($I_{In} = 0$) and the feedback network also does not carry any current ($I_{Fb} = 0$).

Since the OpAmp amplifies the difference between the inputs it tries to bring their difference to zero since the output signal is fed into the inverting input of the OpAmp.

[ U_{out} = U_{in} ]

Note that an amplifier should be unity gain stable to be used with this configuration. Why is this important? The operation of the amplifier itself introduces a 180 degree phase shift (because of the input inversion) - but the propagation delay inside the amplifier also introduces a phase shift. If the phase shift is at 360 degrees one of the Barkhausen criteria for building an oscillator is met - i.e. the amplifier starts to oscillate; note that one should look at the phase shift at all desired (or not filtered) frequencies. Keep in mind that the Barkhausen criteria require 360 degree phase shift as well as an gain above 1 for stable oscillations to occur. One should design feedback circuits in a way to dampen non desired oscillations. Usually one considers the amplifier to be stable for gains larger than one if the phase shift is sufficiently below the Barkhausen limit - usually one uses an limit of 45 degrees to term an circuit as stable.

## Inverting amplifier

The inverting amplifier is one of the basic OpAmp circuits that’s most commonly used. The input is connected to the inverting input via an resistor $R_{In}$, the non inverting input is pulled to signal ground. The output is fed back into the summation point via another feedback resistor $R_f$. The OpAmp tries to output a voltage that pulls the difference between inverting and non inverting input to $0$. Since the optimal internal resistance of the OpAmp is $\infty$ the current flowing into the input has to be exactly the opposite of the current flowing back over the feedback resistor (i.e. the current in the summation point has to vanish) so that the seen voltage at the inverting input is also at ground level:

[ I_{in} = \frac{U_{in}}{R_{in}} \\ I_{F} = - \frac{U_{Out}}{R_{F}} \\ I_{in} = I_{F} \\ \to \frac{U_{in}}{R_{in}} + \frac{U_{Out}}{R_{F}} = 0\\ \to G = \frac{U_{Out}}{U_{in}} = - \frac{R_{in}}{R_{F}} ]

As one can see the voltage gain is determined by the feedback loop. The output signal always has the reverse polarity as the input signal. This configuration in fact also allows for amplification factors smaller than one depending on the configuration.

## Non inverting amplifier

Although the inverting amplifier being the standard circuit for amplifier circuits there is also an non inverting amplifier configuration available. In this case the input is applied to the non inverting input and the output is fed back into the inverting input and to ground via a voltage divider. The main advantage is that the current flowing into the non inverting input is (of course dependent on the OpAmp type) near zero and the configuration also provides an impedance transformer function. As one can see $R_1$ and $R_2$ are composing an voltage divider against ground. One can calculate the total current over the divider since one can again assume that the current into the inverting input of the amplifier is zero and then calculate the voltage drop across both resistors and then require the OpAmp trying to pull the difference between both potentials $U_{in}$ and $U_2$ to zero again:

[ R_t = R_1 + R_2 \\ I_t = \frac{U_out}{R_t} \\ U_1 = R_1 * I_t = U_out * \frac{R_1}{R_1 + R_2} \\ U_2 = R_2 * I_t = U_out * \frac{R_2}{R_1 + R_2} \\ \to U_{in} = U_2 \\ \to U_{in} = U_out * \frac{R_2}{R_1 + R_2} \\ G = \frac{U_{out}}{U_{in}} = \frac{R_1 + R_2}{R_2} \\ \to G = 1 + \frac{R_1}{R_2} ]

As one can see this configuration always has an gain larger than one except for an $R_2 \to \infty$ or $R_1 \to 0$ - which is exactly what the buffer amplifier realizes

## Trans impedance amplifier

The trans impedance amplifier is a circuit that is usually used to measure low currents - for example from a photo-diode - with an high impedance amplifier. Typical amplifiers to use have input impedance in the $T\Omega$ range, for example the ADA4530 (larger than $100 T\Omega$) or the OPA657U (about $10 T\Omega$). These high input impedance lead to leakage currents below $1 pA$ (or even $20 fA$ for the ADA4530). If one measures currents much larger than the leakage current one doesn’t have to account for them, as soon as one gets into the same magnitude leakage currents get relevant and measuring currents below this boundary is not possible.

Again the idea is pretty simple. The current flowing over the current source (i.e. a photo-diode for example) has to be - in the ideal case - the same as the current flowing over the feedback resistor $R_F$. Since the OpAmp tries to pull the inverting input to the same potential as the non inverting input the current that flows over the feedback resistor simply is [ I_{F} = - \frac{U_{out}}{R_F} ]

Since for an optimal OpAmp no current would flow into our out of the inverting input one can assume that the current on the input of the circuit is the only other current flowing out of the summation point:

[ I_{F} = - \frac{U_{out}}{R_F} \\ -I_{S} + I_{F} = 0 \\ \to -\frac{U_{out}}{R_F} = I_{S} \\ \to U_{out} = - I_{S} * R_{F} ]

The selection of the feedback resistor determines the gain. For example if one wants to amplify a current from the $1 nA$ range into about $10 mV$ range one would have to use an resistor of about $10 M\Omega$. But of course one also has to account for the noise. For really low currents one has to carefully follow the recommendations from the datasheets (including board layouts - forget breadboards, do the real thing) and usually use a second and possibly third amplification stage.

Applications in high noise environments (for example particle accelerator instrumentation) keep the pre-amplifiers as close to the measurement points as possible and provide proper shielding - i.e. having the trans impedance amplifier as well as one or two pre-amplification stages there - and sometimes use analog pipelines to shift the signal via an optical converter via fiber outside of the noisy environment in an optical fashion which also solves problems with high bias voltages, etc. Usually you should not do it the following way (even though this turned out to work pretty well): 