Non-inverting Amplifier

Non-inverting Amplifier

The second basic configuration of an operational amplifier circuit is that of a Non-inverting Amplifier. In this configuration, the input voltage signal, (Vin) is applied directly to the Non-inverting (+) 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 and whose output gain is negative in value. Feedback control of the non-inverting amplifier is achieved by applying a small part of the output voltage signal back to the inverting (-) input terminal via a Rf - R2 voltage divider network, again producing negative feedback.

This produces a Non-inverting Amplifier circuit with very good stability, a very high input impedance, Rin approaching infinity (as no current flows into the positive input terminal) and a low output impedance, Rout as shown below.

Non-inverting Amplifier

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, Rf and R2 form a simple voltage divider network across the amplifier and the voltage gain of the circuit is determined by the ratios of R2 and Rf as shown below.

Equivalent Voltage Divider Network

Then using the formula to calculate the output voltage of a potential divider network, we can calculate the output Voltage Gain of the Non-inverting Amplifier as:

Then the closed loop voltage gain of a Non-inverting Amplifier is given as:

We can see that the overall gain of a Non-Inverting Amplifier is greater but never less than 1 (unity), is positive and is determined by the ratio of the values of Rf and R2. If the feedback resistor Rf is zero the gain will be equal to 1 (unity), and if resistor R2 is zero the gain will approach infinity, but in practice it will be limited to the operational amplifiers open-loop differential gain, (A_o).

Voltage Follower (Unity Gain Buffer)

If we made the feedback resistor, Rf = 0 then the circuit will have a fixed gain of "1" and would be classed as a Voltage Follower and this type of Non-inverting amplifier circuit is sometimes called a Voltage follower with gain. As the input signal is connected directly to the non-inverting input of the amplifier the output signal is not inverted resulting in the output voltage being equal to the input voltage, Vout = Vin. This then makes the Voltage Follower circuit ideal as a Unity Gain Buffer circuit because of its isolation properties as impedance or circuit isolation is more important than amplification. The input impedance of the voltage follower circuit is very high, typically above 1MΩ as it is equal to that of the operational amplifiers input, since an ideal op-amp condition is assumed.

In this circuit, Rin has increased to infinity and Rf reduced to zero, the feedback is 100% and Vout is exactly equal to Vin giving it a fixed gain of 1 or unity. As the input voltage Vin is applied to the non-inverting input the gain of the amplifier is given as:

Since no current flows into the non-inverting input terminal the input impedance is infinite and also no current flows through the feedback loop so any value of resistance may be placed in the feedback loop without affecting the characteristics of the circuit as no voltage is dissipated across it, zero current, zero voltage, zero power drop. However in most real unity gain buffer circuits a low value (typically 1kΩ) resistor is required to reduce any offset input leakage currents, and also if the operational amplifier is of a current feedback type.

The voltage follower or unity gain buffer is a special and very useful type of Non-inverting amplifier circuit that is commonly used in electronics to isolated circuits from each other especially in High-order state variable or Sallen-Key type active filters to separate one filter stage from the other. Typical digital buffer IC's available are the 74LS125 Quad 3-state buffer or the more common 74LS244 Octal buffer.

One final thought, the output voltage gain of the voltage follower circuit with closed loop gain is Unity, the voltage gain of an ideal operational amplifier with open loop gain (no feedback) is Infinite. Then by carefully selecting the feedback components we can control the amount of gain produced by an Operational Amplifier anywhere from 1 to infinity.

Inverting Amplifier

We saw in the last tutorial that the Open Loop Gain of an ideal Operational Amplifier can be very high, up to about 1,000,000 (120dB) or more. However, this very high gain is of no real use to us as it makes the amplifier both unstable and hard to control as the smallest of input signals, just a few micro-volts, would be enough to cause the output to saturate and swing towards one or the other of the voltage supply rails losing control. As the open loop DC gain of an operational amplifier is extremely high we can afford to lose some of this 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 system.

Negative Feedback is the process of "feeding back" some of the output signal back to the input, but to make the feedback negative we must feed it back to the "Negative input" terminal using an external Feedback Resistor called Rf. This feedback connection between the output and the inverting input terminal produces a closed loop circuit to the amplifier resulting in the gain of the amplifier now being called its Closed-loop Gain.

This results in the inverting input terminal having a different signal on it than the actual input voltage as it will be the sum of the input voltage plus the negative feedback voltage giving it the label or term of a Summing Point. We must therefore separate the real input signal from the inverting input by using an Input Resistor, Rin. As we are not using the positive non-inverting input this is connected to a common ground or zero voltage terminal as shown below, but the effect of this closed loop feedback circuit results in the voltage potential at the inverting input being equal to that at the non-inverting input producing a Virtual Earth summing point because it will be at the same potential as the grounded reference input.

Inverting Amplifier Circuit

In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. There are two very important rules to remember about inverting amplifiers is that, "no current flows into the input terminal" and that "V1 equals V2". This is because the junction of the input and feedback signal (X) is at the same potential as the positive (+) input which is at zero volts or ground then, the junction is a "Virtual Earth". Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.

We said above that there are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and they are.

• 1. No Current Flows into the Input Terminals
• 2. The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth)

Then by using these two rules we can find the equation for calculating the gain of an inverting amplifier, using first principles.

Current ( i ) flows through the resistor network as shown.

Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as.

and this can be transposed to give:

The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180^o out of phase. This is due to the feedback being negative in value.

Example No1

Find the closed loop gain of the following inverting amplifier circuit.

Using the previously found formula for the gain of the circuit

we can now substitute the values of the resistors in the circuit as follows,

Rin = 10kΩ and Rf = 100kΩ.

and the gain of the circuit is calculated as -Rf/Rin = 100k/10k = 10.

therefore, the closed loop gain of the inverting amplifier circuit above is given 10 or 20dB.

Example No2.

The gain of the original circuit is to be increased to 40, find the new values of the resistors required.

Assume that the input resistor is to remain at the same value of 10KΩ, then by re-arranging the closed loop voltage gain formula we can find the new value required for the feedback resistor Rf.

Gain = -Rf/Rin

therefore, Rf = Gain x Rin

Rf = 40 x 10,000

Rf = 400,000 or 400KΩ

The new values of resistors required for the circuit to have a gain of 40 would be,

Rin = 10KΩ and Rf = 400KΩ.

The formula could also be rearranged to give a new value of Rin, keeping the same value of Rf.

One final point to note about Inverting Amplifiers, if the two resistors are of equal value, Rin = Rf then the gain of the amplifier will be -1 producing a complementary form of the input voltage at its output as Vout = -Vin. This type of inverting amplifier configuration is generally called a Unity Gain Inverter of simply an Inverting Buffer.

Ideal Operational Amplifier

As well as resistors and capacitors, Operational Amplifiers, or Op-amps as they are more commonly called, are one of the basic building blocks of Analogue Electronic Circuits. It is a linear device that has all the properties required for nearly ideal DC amplification and is 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 3-terminal device that consists of two high impedance inputs, one an Inverting input marked with a negative sign, ("-") and the other a Non-inverting input marked with a positive plus sign ("+").

The amplified output signal of an Operational Amplifier is the difference between the two signals being applied to the two inputs. In other words the output signal is a differential signal between the two inputs and the input stage of an Operational Amplifier is in fact a differential amplifier as shown below.

Differential Amplifier

The circuit shows a generalized form of a differential amplifier with two inputs marked V1 and V2. The two identical transistors TR1 and TR2 are both biased at the same operating point with their emitters connected together and returned to the common rail, -Vee by way of resistor Re. The circuit operates from a dual supply +Vcc and -Vee which ensures a constant supply. The voltage that appears at the output, Vout of the amplifier is the difference between the two input signals as the two base inputs are in anti-phase with each other. So as the forward bias of transistor, TR1 is increased, the forward bias of transistor TR2 is reduced and vice versa. Then if the two transistors are perfectly matched, the current flowing through the common emitter resistor, Re will remain constant.

Like the input signal, the output signal is also balanced and since the collector voltages either swing in opposite directions (anti-phase) or in the same direction (in-phase) the output voltage signal, taken from between the two collectors is, assuming a perfectly balanced circuit the zero difference between the two collector voltages. This is known as the Common Mode of Operation with the common mode gain of the amplifier being the output gain when the input is zero.

Ideal Operational Amplifiers also have one output (although there are ones with an additional differential output) of low impedance that is referenced to a common ground terminal and it should ignore any common mode signals that is, if an identical signal is applied to both the inverting and non-inverting inputs there should no change to the output. However, in real amplifiers there is always some variation and the ratio of the change to the output voltage with regards to the change in the common mode input voltage is called the Common Mode Rejection Ratio or CMRR.

Operational Amplifiers on their own have a very high open loop DC gain and by applying some form of Negative Feedback we can produce an operational amplifier circuit that has a very precise gain characteristic that is dependant only on the feedback used. An operational amplifier only responds to the difference between the voltages on its two input terminals, known commonly as the "Differential Input Voltage" and not to their common potential. Then if the same voltage potential is applied to both terminals the resultant output will be zero. An Operational Amplifiers gain is commonly known as the Open Loop Differential Gain, and is given the symbol (A_o).

Equivalent Circuit for Ideal Operational Amplifiers

Idealized Characteristics.

PARAMETER	IDEALIZED CHARACTERISTIC
Voltage Gain, (A)	Infinite - The main function of an operational amplifier is to amplify the input signal and the more open loop gain it has the better, so for an ideal amplifier the gain will be infinite.
Input impedance, (Zin)	Infinite - Input impedance is assumed to be infinite to prevent any current flowing from the source supply into the amplifiers input circuitry.
Output impedance, (Zout)	Zero - The output impedance of the ideal operational amplifier is assumed to be zero so that it can supply as much current as necessary to the load.
Bandwidth, (BW)	Infinite - An ideal operational amplifier has an infinite Frequency Response and can amplify any frequency signal so it is assumed to have an infinite bandwidth.
Offset Voltage, (Vio)	Zero - The amplifiers output will be zero when the voltage difference between the inverting and non-inverting inputs is zero.

From these "idealized" characteristics above, we can see that the input resistance is infinite, so no current flows into either input terminal (the current rule) and that the differential input offset voltage is zero (the voltage rule). It is important to remember these two properties as they help understand the workings of the amplifier with regards to analysis and design of operational amplifier circuits.

However, real Operational Amplifiers such as the commonly available uA741, for example do not have infinite gain or bandwidth but have a typical "Open Loop Gain" which is defined as the amplifiers output amplification without any external feedback signals connected to it and for a typical operational amplifier is about 100dB at DC (zero Hz). This output gain decreases linearly with frequency down to "Unity Gain" or 1, at about 1MHz and this is shown in the following open loop gain response curve.

Open-loop Frequency Response Curve

From this frequency response curve we can see that the product of the gain against frequency is constant at any point along the curve. Also that the unity gain (0dB) frequency also determines the gain of the amplifier at any point along the curve. This constant is generally known as the Gain Bandwidth Product or GBP.

Therefore, GBP = Gain x Bandwidth or A x BW.

For example, from the graph above the gain of the amplifier at 100kHz = 20dB or 10, then the

GBP = 100,000Hz x 10 = 1,000,000.

Similarly, a gain at 1kHz = 60dB or 1000, therefore the

GBP = 1,000 x 1,000 = 1,000,000. The same!.

The Voltage Gain (A) of the amplifier can be found using the following formula:

and in Decibels or (dB) is given as:

An Operational Amplifiers Bandwidth

The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% or -3dB (where 0dB is the maximum) of its maximum output value as shown below.

Here we have used the 40dB line as an example. The -3dB or 70.7% of Vmax down point from the frequency response curve is given as 37dB. Taking a line across until it intersects with the main GBP curve gives us a frequency point just above the 10kHz line at about 12 to 15kHz. We can now calculate this more accurately as we already know the GBP of the amplifier, in this particular case 1MHz.

Example No1.

Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as:

37 = 20 log A therefore, A = anti-log (37 ÷ 20) = 70.8

GBP ÷ A = Bandwidth, therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz

Then the bandwidth of the amplifier at a gain of 40dB is given as 14kHz as previously predicted from the graph.

Example No2.

If the operational amplifiers gain was reduced by half to say 20dB in the above frequency response curve, the -3dB point would now be at 17dB. This would then give us an overall gain of 7.08, therefore A = 7.08. If we use the same formula as above this new gain would give us a bandwidth of 141.2kHz, ten times more than at 40dB. It can therefore be seen that by reducing the overall open loop gain of an operational amplifier its bandwidth is increased and visa versa. The -3dB point is also known as the "half power point", as the output power of the amplifier is at half its maximum value at this point.

Op-amp types

Operational amplifiers can be connected using external resistors or capacitors in a number of different ways to form basic "building Block" circuits such as, Inverting, Non-Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type amplifiers. There are a very large number of operational amplifier IC's available to suit every possible application such as bipolar standard, precision, high-speed, low-noise, high-voltage, etc and again with internal JFET transistors.

The most commonly available and used of all operational amplifiers is the industry standard μA-741.