What About Lesson number one Operational Amplifier Basics 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. They are used in signal conditioning, filtering or to perform mathematical operations such as add, subtract, integration and differentiation. An ideal Operational Amplifier is basically a three-terminal 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 Non-inverting Input, marked with a positive or plus sign ( + ). The third terminal represents the output port. The amplified output signal of an Operational Amplifier is the difference between the two signals being applied to the two inputs multiplied by the Open Loop Differential Gain, called A OL. In a linear operational amplifier, the output signal V out is the input signal V in multiplied by the value of amplification factor, known as the amplifiers gain A v. Equivalent Circuit for Ideal Operational Amplifiers 1
Op-amp Parameter Open Loop Gain (A OL ) o typical real values range from about 20,000 to 200,000. Input impedance (Z in ) The input resistance is very high, (2MΩ for the µa741) so no current flows into either input terminal and that the differential input offset voltage is zero. Output impedance (Z out ) The output resistance is very low, (75Ω for the µa741) Bandwidth, (BW) o the bandwidth is limited by the Gain-Bandwidth product (GB), which is equal to the frequency where the amplifiers gain becomes unity (1MHz for the µa741). 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. The Voltage Gain (A V ) of the operational amplifier can be found using the following formula: and in Decibels or (db) is given as: 2
The most commonly available and used of all operational amplifiers in basic electronic kits and projects is the industry standard μa-741. The Inverting Operational Amplifier The Open Loop Gain of an operational amplifier can be very high so we can reduce it by connecting an external Feedback Resistor called Rƒ across the amplifier from the output terminal back to the inverting input terminal to control the gain of the amplifier. The effect known as Negative Feedback produces a closed loop circuit: the gain of the amplifier now is called Closed-loop Gain. As we are not using the positive non-inverting input this is connected to a common ground, 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. The closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors. 3
There are two very important rules to remember about Inverting Amplifiers or any operational amplifier: 1. No Current Flows into the Input Terminals 2. The Differential Input Voltage is Zero as V 1 = V 2 = 0 (Virtual Earth) The current flows through the resistor network as shown. Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as. 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. 4
The Non-inverting Operational Amplifier The second basic configuration of an operational amplifier circuit is that of a Noninverting Operational 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. The result of this is that the output signal is in-phase with the input signal. Then using the formula to calculate the output voltage of a potential divider network, we can calculate the closed-loop voltage gain ( A V ) of the Non-inverting Amplifier as follows: Then the closed loop voltage gain of a Non-inverting Operational Amplifier will be given as: We can see from the equation above, that the closed-loop gain of a non-inverting amplifier will always be greater than one (unity). 5
Voltage Follower (Unity Gain Buffer) If we made the feedback resistor, Rƒ equal to zero, (Rƒ = 0), and resistor R 2 equal to infinity, (R 2 = ), then the circuit would have a fixed gain of 1 as all the output voltage would be present on the inverting input terminal (negative feedback). This would then produce a special type of the non-inverting amplifier circuit called a Voltage Follower or also called a unity gain buffer : the input impedance is very high and the output impedance is very low. Non-inverting Voltage Follower Differential Amplifier Thus far we have used only one of the operational amplifiers inputs to connect to the amplifier, using either the inverting or the non-inverting 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. Basically, as we saw in the first tutorial about Operational Amplifiers, all op-amps are Differential Amplifiers due to their input configuration. But by connecting one voltage signal onto one input terminal and another voltage signal onto the other input terminal the resultant output voltage will be proportional to the Difference between the two input voltage signals of V1 and V2. 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. This type of operational amplifier circuit is commonly known as a Differential Amplifier configuration and is shown below: 6
By connecting each input in turn to 0v ground we can use superposition to solve for the output voltage Vout. Then the transfer function for a Differential Amplifier circuit is given as: When resistors, R1 = R2 and R3 = R4 the above transfer function for the differential amplifier can be simplified to the following expression: 7
Differential Amplifier Equation 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 output voltage sum will be negative, and if V2 is higher than V1, the output voltage sum will be positive. The Differential Amplifier circuit is a very useful op-amp circuit and by adding more resistors in parallel with the input resistors R1 and R3, the resultant circuit can be made to either Add or Subtract the voltages applied to their respective inputs. One of the most common ways of doing this is to connect a Resistive Bridge commonly called a Wheatstone Bridge to the input of the amplifier as shown below. 8
Operational Amplifiers Summary The Operational Amplifier, or Op-amp as it is most commonly called, is an ideal amplifier with infinite Gain and Bandwidth when used in the Open-loop mode with typical DC gains of well over 100,000. 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 a low output impedance. Op-amps sense the difference between the voltage signals applied to their two input terminals and then multiply it by some pre-determined Open-loop Gain. Closing the open loop by connecting a resistive or reactive component between the output and one input terminal of the op-amp greatly reduces and controls this open-loop gain. For negative feedback, were the fed-back voltage is in anti-phase to the input the overall gain of the amplifier is reduced. For positive feedback, were the fed-back voltage is in Phase with the input the overall gain of the amplifier is increased. By connecting the output directly back to the negative input terminal, 100% feedback is achieved resulting in a Voltage Follower (buffer) circuit with a constant gain of 1 (Unity). Changing the fixed feedback resistor ( Rƒ ) for a Potentiometer, the circuit will have Adjustable Gain. Operational Amplifier Gain 9
The Open-loop gain called the Gain Bandwidth Product can be very high and is a measure of how good an amplifier is. By the use of a suitable feedback resistor, ( Rƒ ) the overall gain of the amplifier can be accurately controlled. By adding more input resistors to either the inverting or non-inverting inputs Voltage Adders or Summers can be made. Voltage follower op-amps can be added to the inputs of Differential amplifiers to produce high impedance Instrumentation amplifiers. The Differential Amplifier produces an output that is proportional to the difference between the 2 input voltages. 10
The Integrator Amplifier produces an output that is the mathematical operation of integration. The Differentiator Amplifier produces an output that is the mathematical operation of differentiation. Both the Integrator and Differentiator Amplifiers have a resistor and capacitor connected across the opamp and are affected by its RC time constant. 11
Inverting Op-amp Example N o 1 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, R in = 10kΩ and R ƒ = 100kΩ. and the gain of the circuit is calculated as -R ƒ /R in = 100k/10k = -10. therefore, the closed loop gain of the inverting amplifier circuit above is given -10. Inverting Op-amp Example N o 2 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 Rƒ. Gain = -R ƒ /R in therefore, R ƒ = Gain x R in R ƒ = 40 x 10,000 = 400,000 or 400KΩ The new values of resistors required for the circuit to have a gain of 40 would be R in = 10KΩ and R ƒ = 400KΩ. 12