Operational amplifiers are simple to use, inexpensive and offer a very large amount of gain. LM741 IC is the most common Op Amp. Op Amps have two inputs called the non-inverting and the inverting designated by the plus and minus sign, respectively. Op Amps are actually differential amplifiers because they amplify the difference between the inverting and the non-inverting inputs. Op amps will normally operate from any supply voltage in the 6 to 15 volt range.
Setting The Gain of The Op Amp
The gain of this circuit is determined by resistors R1 and R2 and is calculated by the following equation:
Voltage Gain = R2 / R1
R1 can be any value from 470 to 10K. Because Op Amps have input impedances as high as several hundred thousand ohms or greater, any input power lost through R1 is insignificant. R2 can be any value from 10K to 1M. R2 actually limits the gain of the Op Amp by providing a form of negative feedback. Op Amps typically have voltage gains between 20,000 to 200,000. In no case should the voltage gain set by R2 / R1 be greater than 1,000. The voltage gain is essentially independent of the supply voltage.
NON-INVERTING AND INVERTING 741 AMPLIFIERS
1. An inverting amplifier - Leg two is the input and the output is always reversed or inverted.
2. A Non-inverting amplifier - Leg three is the input and the output is not reversed.
Opposite is a diagram of an INVERTING AMPLIFIER.
This means that if the voltage going into the 741 chip is positive, it is negative when it comes out of the 741. In other words it reverses polarity (inverts polarity).
Two resistors are needed to make the 741 work as an amplifier, R1 and R2. In most text books diagrams like this are used to represent the 741.
This means that if the voltage going into the 741 chip is positive, it is negative when it comes out of the 741. In other words it reverses polarity (inverts polarity).
Two resistors are needed to make the 741 work as an amplifier, R1 and R2. In most text books diagrams like this are used to represent the 741.
The Inverting Operational Amplifier
We saw in the last tutorial that the Open Loop Gain, ( Avo ) of an operational amplifier can be very high, as much as 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, (μV) would be enough to cause the output voltage to saturate and swing towards one or the other of the voltage supply rails losing complete control of the output.
As the open loop DC gain of an Operational Amplifiers 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 op-amp 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 Closed-loop Gain. Then a closed-loop inverting amplifier uses negative feedback to accurately control the overall gain of the amplifier, but at a cost in the reduction of the amplifiers gain.
This negative feedback 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 aVirtual Earth summing point because it will be at the same potential as the grounded reference input. In other words, the op-amp becomes a “differential amplifier”.
Inverting Operational Amplifier Configuration
In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. When dealing with operational amplifiers there are two very important rules to remember about inverting amplifiers, these are: “No current flows into the input terminal” and that “V1 always equals V2”. However, in real world op-amp circuits both of these rules are slightly broken.
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 these 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 derive the equation for calculating the closed-loop 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 Vout as:
Linear Output
The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value.
The equation for the output voltage Vout also shows that the circuit is linear in nature for a fixed amplifier gain as Vout = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.
Another useful application of an inverting amplifier is that of a “transresistance amplifier” circuit. A Transresistance Amplifier also known as a “transimpedance amplifier”, is basically a current-to-voltage converter (Current “in” and Voltage “out”). They can be used in low-power applications to convert a very small current generated by a photo-diode or photo-detecting device etc, into a usable output voltage which is proportional to the input current as shown.
Transresistance Amplifier Circuit
The simple light-activated circuit above, converts a current generated by the photo-diode into a voltage. The feedback resistor Rƒ sets the operating voltage point at the inverting input and controls the amount of output. The output voltage is given as Vout = Is x Rƒ. Therefore, the output voltage is proportional to the amount of input current generated by the photo-diode.
The Non-inverting Operational Amplifier
The second basic configuration of an operational amplifier circuit is that of a Non-inverting 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 in contrast to the “Inverting Amplifier” . The result of this is that the output signal is “in-phase” with the input signal.
Feedback control of the Non-inverting Operational 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 closed-loop configuration 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, (ideal conditions) and a low output impedance, Rout as shown below.
n the previous Inverting Amplifier tutorial, we said that for an ideal op-amp “No current flows into the input terminal” of the amplifier and that “V1 always 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 non-inverting amplifier with the voltage gain of the circuit being determined by the ratios of R2 and Rƒ as shown below.
Equivalent Potential Divider Network
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 overall closed-loop gain of a non-inverting amplifier will always be greater but never less than one (unity), it is positive in nature and is determined by the ratio of the values of Rƒ and R2.
If the value of the feedback resistor Rƒ is zero, the gain of the amplifier will be exactly equal to one (unity). 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, ( Ao ).
We can easily convert an inverting operational amplifier configuration into a non-inverting amplifier configuration by simply changing the input connections as shown.
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Basic Comparator Operation
Input Vs. Output Results
- Current WILL flow through the open collector when the voltage at the PLUS input is lower than the voltage at the MINUS input.
- Current WILL NOT flow through the open collector when the voltage at the PLUS input is higher than the voltage at the MINUS input.
Comparator Operation
The following drawing show the two simplest configurations for voltage comparators. The diagrams below the circuits give the output results in a graphical form. For these circuits the REFERENCE voltage is fixed at one-half of the supply voltage while the INPUT voltage is variable from zero to the supply voltage.
In theory the REFERENCE and INPUT voltages can be anywhere between zero and the supply voltage but there are practical limitations on the actual range depending on the particular device used.
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Op Amp as Schmitt Trigger
Working
When the output of Op Amp is high, the threshold voltage will be about 2.5V, and when it is low, the threshold voltage will be 1.67 (=5/3) volts (figure it out). This creates two separate thresholds. If we apply the same input to this new circuit, we now get one transition of the output, because of the changing threshold voltage. (When the output is high, the threshold is high --
when the output is low, the threshold is low). Note that the output now only goes up to 2.5 volts. Make sure you understand how this circuit works. It is a bit tricky both because the circuit is non-linear, and because the value of the output is not a single-valued function of the input. This is manifested by the fact that the output can either be high (2.5 volts) or low (0 volts) when the input is between 1.67 and 2.5 volts.
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The basic electrical operation of an Active High Pass Filter (HPF) is exactly the same as equivalent RC passive high pass filter circuit, except this time the circuit has an operational amplifier or op-amp included within its filter design providing amplification and gain control.
First Order Active High Pass Filter
Technically, there is no such thing as an active high pass filter. Unlike Passive High Pass Filterswhich have an “infinite” frequency response, the maximum pass band frequency response of anActive High Pass Filter is limited by the open-loop characteristics or bandwidth of the operational amplifier being used, making them appear as if they are band pass filters with a high frequency cut-off determined by the selection of op-amp and gain.
In the Operational Amplifier tutorial we saw that the maximum frequency response of an op-amp 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 “open-loop” (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 op-amp to have a frequency response curve very similar to that of a first-order low pass filter and this is shown below.
Frequency response curve of a typical Operational Amplifier.
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The principle of operation and frequency response of an Active Low Pass Filter exactly the same as passive filter, the only difference is that it uses an op-amp for amplification and gain control. The simplest form of a low pass active filter is to connect an inverting or non-inverting amplifier, with an input basic RC low pass filter circuit:
First Order Active Low Pass Filter
This consists of a passive RC filter stage providing a low frequency path to the input of a non-inverting amplifier. The amplifier is configured as a voltage-follower its DC gain of one, Av = +1.
In this configuration the op-amps high input impedance prevents excessive loading on the filters output while its low output impedance prevents the filters cut-off frequency point from being affected by changes in the impedance of the load.
While its major disadvantage is that it has no voltage gain above one. However, although the voltage gain is unity the power gain is very high as its output impedance is much lower than its input impedance.
Active Low Pass Filter with Amplification
The frequency response of the circuit will be the same as that for the passive RC filter, except that the amplitude of the output is increased by the pass band gain, AF of the amplifier. For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor ( R2) divided by its corresponding input resistor ( R1) value and is given as:
Therefore, the gain of an active low pass filter as a function of frequency will be:
- Where:
- AF = the pass band gain of the filter, (1 + R2/R1)
- ƒ = the frequency of the input signal in Hertz, (Hz)
- ƒc = the cut-off frequency in Hertz, (Hz)
Thus, the operation of a low pass active filter can be verified from the frequency gain equation above as:
- 1. At very low frequencies, ƒ < ƒc
- 2. At the cut-off frequency, ƒ = ƒc
- 3. At very high frequencies, ƒ > ƒc
Thus, the Active Low Pass Filter has a constant gain AF from 0Hz to the high frequency cut-off point,ƒC. At ƒC the gain is 0.707AF, and after ƒC it decreases at a constant rate as the frequency increases. That is, when the frequency is increased tenfold (one decade), the voltage gain is divided by 10.
Low Pass Filter Circuit.
Second-order Active Low Pass Filter Circuit
When cascading together filter circuits to form higher-order filters, the overall gain of the filter is equal to the product of each stage. For example, the gain of one stage may be 10 and the gain of the second stage may be 32 and the gain of a third stage may be 100. Then the overall gain will be 32,000, (10 x 32 x 100)
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