
 The Operational Amplifier, or Opamp as it is most commonly called, is an ideal amplifier with infinite Gain and Bandwidth when used in the Openloop mode with typical d.c. gains of well over 100,000, or 100dB.
 The basic Opamp construction is of a 3terminal device, 2inputs and 1output.
 An Operational Amplifier operates from either a dual positive ( +V ) and an corresponding negative ( V ) supply, or they can operate from a single DC supply voltage.
 The two main laws associated with the operational amplifier are that it has an infinite input impedance, ( Z∞ ) resulting in "No current flowing into either of its two inputs" and zero input offset voltage "V1 = V2".
 An operational amplifier also has zero output impedance, ( Z = 0 ).
 Opamps sense the difference between the voltage signals applied to their two input terminals and then multiply it by some predetermined Gain, ( A ).
 This Gain, ( A ) is often referred to as the amplifiers "Openloop Gain".
 Closing the open loop by connecting a resistive or reactive component between the output and one input terminal of the opamp greatly reduces and controls this openloop gain.
 Opamps can be connected into two basic configurations, Inverting and Noninverting.

 The Openloop gain called the Gain Bandwidth Product, or (GBP) can be very high and is a measure of how good an amplifier is.
 Very high GBP makes an operational amplifier circuit unstable as a micro volt input signal causes the output voltage to swing into saturation.
 By the use of a suitable feedback resistor, ( Rƒ ) the overall gain of the amplifier can be accurately controlled.

 For negative feedback, were the fedback voltage is in "antiphase" to the input the overall gain of the amplifier is reduced.
 For positive feedback, were the fedback voltage is in "Phase" with the input the overall gain of the amplifier is increased.

The basic Opamp Differentiator circuit is the exact opposite to that of the Integrator operational amplifier circuit that we saw in the previous tutorial. Here, the position of the capacitor and resistor have been reversed and now the reactance, Xc is connected to the input terminal of the inverting amplifier while the resistor, Rƒ forms the negative feedback element across the operational amplifier as normal

This circuit performs the mathematical operation of Differentiation, that is it "produces a voltage output which is directly proportional to the input voltage's rateofchange with respect to time". In other words the faster or larger the change to the input voltage signal, the greater the input current, the greater will be the output voltage change in response, becoming more of a "spike" in shape.

The input signal to the differentiator is applied to the capacitor. The capacitor blocks any DC content so there is no current flow to the amplifier summing point, X resulting in zero output voltage. The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependant on the rate of change of the input signal.

In the previous tutorials we have seen circuits which show how an operational amplifier can be used as part of a positive or negative feedback amplifier or as an adder or subtractor type circuit using just pure resistances in both the input and the feedback loop. But what if we were to change the purely resistive ( Rƒ ) feedback element of an inverting amplifier to that of a frequency dependant impedance, ( Z ) type complex element, such as a Capacitor, C. What would be the effect on the output voltage. By replacing this feedback resistance with a capacitor we now have an RC Network across the operational amplifier producing an Opamp Integrator circuit as shown below.

As its name implies, the Opamp Integrator is an operational amplifier circuit that performs the mathematical operation of Integration, that is we can cause the output to respond to changes in the input voltage over time as the opamp integrator produces an output voltage which is proportional to the integral of the input voltage.

In other words the magnitude of the output signal is determined by the length of time a voltage is present at its input as the current through the feedback loop charges or discharges the capacitor as the required negative feedback occurs through the capacitor.

Thus far we have used only one of the operational amplifiers inputs to connect to the amplifier, using either the "inverting" or the "noninverting" input terminal to amplify a single input signal with the other input being connected to ground. But we can also connect signals to both of the inputs at the same time producing another common type of operational amplifier circuit called a Differential Amplifier.

Then differential amplifiers amplify the difference between two voltages making this type of operational amplifier circuit a Subtractor unlike a summing amplifier which adds or sums together the input voltages.

If all the resistors are all of the same ohmic value, that is: R1 = R2 = R3 = R4 then the circuit will become a Unity Gain Differential Amplifier and the voltage gain of the amplifier will be exactly one or unity. Then the output expression would simply be Vout = V2  V1. Also note that if input V1 is higher than input V2 the ouput voltage sum will be negative, and if V2 is higher than V1, the output voltage sum will be positive.

The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifier configuration that can be used for combining multiple inputs. We saw previously in the inverting amplifier tutorial that the inverting amplifier has a single input voltage, ( Vin ) applied to the inverting input terminal. If we add more input resistors to the input, each equal in value to the original input resistor, Rin we end up with another operational amplifier circuit called a Summing Amplifier, "summing inverter" or even a "voltage adder" circuit as shown below.

The output voltage, ( Vout ) now becomes proportional to the sum of the input voltages, V1, V2, V3 etc

Summing Amplifier Equation

The second basic configuration of an operational amplifier circuit is that of a Noninverting Amplifier. In this configuration, the input voltage signal, ( Vin ) is applied directly to the noninverting ( + ) input terminal which means that the output gain of the amplifier becomes "Positive" in value in contrast to the "Inverting Amplifier" circuit we saw in the last tutorial whose output gain is negative in value. The result of this is that the output signal is "inphase" with the input signal.

Feedback control of the noninverting amplifier is achieved by applying a small part of the output voltage signal back to the inverting (  ) input terminal via a Rƒ  R2 voltage divider network, again producing negative feedback. This closedloop configuration produces a noninverting amplifier circuit with very good stability, a very high input impedance, Rin approaching infinity, as no current flows into the positive input terminal, (ideal conditions) and a low output impedance, Rout as shown below.

In the previous Inverting Amplifier tutorial, we said that "no current flows into the input" of the amplifier and that "V1 equals V2". This was because the junction of the input and feedback signal ( V1 ) are at the same potential. In other words the junction is a "virtual earth" summing point. Because of this virtual earth node the resistors, Rƒ and R2 form a simple potential divider network across the noninverting amplifier with the voltage gain of the circuit being determined by the ratios of R2 and Rƒ as shown below.

As the open loop DC gain of an operational amplifier is extremely high we can therefore afford to lose some of this high gain by connecting a suitable resistor across the amplifier from the output terminal back to the inverting input terminal to both reduce and control the overall gain of the amplifier. This then produces and effect known commonly as Negative Feedback, and thus produces a very stable Operational Amplifier based system.

Negative Feedback is the process of "feeding back" a fraction of the output signal back to the input, but to make the feedback negative, we must feed it back to the negative or "inverting input" terminal of the opamp using an external Feedback Resistor called Rƒ. This feedback connection between the output and the inverting input terminal forces the differential input voltage towards zero.

This effect produces a closed loop circuit to the amplifier resulting in the gain of the amplifier now being called its Closedloop Gain. Then a closedloop inverting amplifier uses negative feedback to accurately control the overall gain of the amplifier, but at a cost in the reduction of the amplifiers bandwidth.

As well as resistors and capacitors, Operational Amplifiers, or Opamps as they are more commonly called, are one of the basic building blocks of Analogue Electronic Circuits. Operational amplifiers are linear devices that have all the properties required for nearly ideal DC amplification and are therefore used extensively in signal conditioning, filtering or to perform mathematical operations such as add, subtract, integration and differentiation.

An ideal Operational Amplifier is basically a threeterminal device which consists of two high impedance inputs, one called the Inverting Input, marked with a negative or "minus" sign, (  ) and the other one called the Noninverting Input, marked with a positive or "plus" sign ( + ).

 Voltage – Voltage "in" and Voltage "out"
 Current – Current "in" and Current "out"
 Transconductance – Voltage "in" and Current "out"
 Transresistance – Current "in" and Voltage "out"
The third terminal represents the opamps output port which can both sink and source either a voltage or a current. In a linear operational amplifier, the output signal is the amplification factor, known as the amplifiers gain ( A ) multiplied by the value of the input signal and depending on the nature of these input and output signals, there can be four different classifications of operational amplifier gain.

In the previous sections we looked at simple firstorder type low and high pass filters that contain only a single resistor and a single reactive component (a capacitor) within their circuit design. In applications that use filters to shape the frequency spectrum of a signal such as in communications or control systems, the shape or width of the rolloff also called the "transition band", for a simple firstorder filter may be too long or wide and so active filters designed with more than one "order" are required. These types of filters are commonly known as "Highorder" or "n^{th}order" filters.

The complexity or filter type is defined by the filters "order", and which is dependant upon the number of reactive components such as capacitors or inductors within its design. We also know that the rate of rolloff and therefore the width of the transition band, depends upon the order number of the filter and that for a simple firstorder filter it has a standard rolloff rate of 20dB/decade or 6dB/octave.

One final comment about Decades and Octaves. On the frequency scale, a Decade is a tenfold increase (multiply by 10) or tenfold decrease (divide by 10). For example, 2 to 20Hz represents one decade, whereas 50 to 5000Hz represents two decades (50 to 500Hz and then 500 to 5000Hz).

In a Band Pass Filter circuit, the overall width of the actual pass band between the upper and lower 3dB corner points of the filter determines the Quality Factor or Qpoint of the circuit. This Q Factor is a measure of how "Selective" or "Unselective" the band pass filter is towards a given spread of frequencies. The lower the value of the Q factor the wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more "selective" is the filter.

Technically, there is no such thing as an active high pass filter. Unlike Passive High Pass Filters which have an "infinite" frequency response, the maximum pass band frequency response of an active high pass filter is limited by the openloop characteristics or bandwidth of the operational amplifier being used, making them appear as if they are band pass filters with a high frequency cutoff determined by the selection of opamp and gain

In the Operational Amplifier tutorial we saw that the maximum frequency response of an opamp is limited to the Gain/Bandwidth product or open loop voltage gain ( A_{ V} ) of the operational amplifier being used giving it a bandwidth limitation, where the closed loop response of the op amp intersects the open loop response.

A commonly available operational amplifier such as the uA741 has a typical "openloop" (without any feedback) DC voltage gain of about 100dB maximum reducing at a roll off rate of 20dB/Decade (6db/Octave) as the input frequency increases. The gain of the uA741 reduces until it reaches unity gain, (0dB) or its "transition frequency" ( ƒt ) which is about 1MHz. This causes the opamp to have a frequency response curve very similar to that of a firstorder low pass filter and this is shown below.

An active filter generally uses an operational amplifier (opamp) within its design and in the Operational Amplifier tutorial we saw that an Opamp has a high input impedance, a low output impedance and a voltage gain determined by the resistor network within its feedback loop.

Unlike a passive high pass filter which has in theory an infinite high frequency response, the maximum frequency response of an active filter is limited to the Gain/Bandwidth product (or open loop gain) of the operational amplifier being used.

This firstorder low pass active filter, consists simply of a passive RC filter stage providing a low frequency path to the input of a noninverting operational amplifier. The amplifier is configured as a voltagefollower (Buffer) giving it a DC gain of one, Av = +1 or unity gain as opposed to the previous passive RC filter which has a DC gain of less than unity.

Clearly for a pass band filter to function correctly, the cutoff frequency of the low pass filter must be higher than the cutoff frequency for the high pass filter.

Band pass filters are known generally as secondorder filters, (twopole) because they have "two" reactive component, the capacitors, within their circuit design. One capacitor in the low pass circuit and another capacitor in the high pass circuit.

The point of maximum output gain is generally the geometric mean of the two 3dB value between the lower and upper cutoff points and is called the "Centre Frequency" or "Resonant Peak" value ƒr. This geometric mean value is calculated as being ƒr^{ 2} = ƒ_{(UPPER)} x ƒ_{(LOWER)}.

Where the low pass filter only allowed signals to pass below its cutoff frequency point, ƒc, the passive high pass filter circuit as its name implies, only passes signals above the selected cutoff point, ƒc eliminating any low frequency signals from the waveform

In this circuit arrangement, the reactance of the capacitor is very high at low frequencies so the capacitor acts like an open circuit and blocks any input signals at Vin until the cutoff frequency point ( ƒc ) is reached. Above this cutoff frequency point the reactance of the capacitor has reduced sufficiently as to now act more like a short circuit allowing all of the input signal to pass directly to the output as shown below in the High Pass Frequency Response Curve.

The High Pass Filter is the exact opposite to the low pass filter. This filter has no output voltage from DC (0Hz), up to a specified cutoff frequency ( ƒc ) point. This lower cutoff frequency point is 70.7% or 3dB (dB = 20log Vout/Vin) of the voltage gain allowed to pass. The frequency range "below" this cutoff point ƒc is generally known as the Stop Band while the frequency range "above" this cutoff point is generally known as the Pass Band.

In low frequency applications (up to 100kHz), passive filters are generally constructed using simple RC (ResistorCapacitor) networks, while higher frequency filters (above 100kHz) are usually made from RLC (ResistorInductorCapacitor) components. Passive filters are made up of passive components such as resistors, capacitors and inductors and have no amplifying elements (transistors, opamps, etc) so have no signal gain, therefore their output level is always less than the input.

Simple Firstorder passive filters (1st order) can be made by connecting together a single resistor and a single capacitor in series across an input signal, ( Vin ) with the output of the filter, ( Vout ) taken from the junction of these two components. Depending on which way around we connect the resistor and the capacitor with regards to the output signal determines the type of filter construction resulting in either a Low Pass Filter or a High Pass Filter.

Filters can be divided into two distinct types: active filters and passive filters. Active filters contain amplifying devices to increase signal strength while passive do not contain amplifying devices to strengthen the signal. As there are two passive components within a passive filter design the output signal has a smaller amplitude than its corresponding input signal, therefore passive RC filters attenuate the signal and have a gain of less than one, (unity).
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