Unit 35 P4 & P7 Exemplar Report
Introduce the Task
This task requires us to build, test and simulate a non-inverting amplifier based on an LM741. From the task list we will be:
- Proving that the gain of the amplifier is given by 1+R1/R2
- Finding the Gain Bandwidth Product of the amplifier and finding the bandwidth of an amplifier with a gain of 25
- Building the circuit on breadboard and carrying out the same tests on the physical circuit
- Comparing and contrasting the results and confirming their relation to theory
We first built the circuit in Multisim. The basic circuit is shown below:
This is an amplifier circuit. An amplifier makes the output voltage at pin 6 bigger than the input voltage at pin 3. When an amplifier makes a signal bigger we call it the gain of the amplifier.
Gain is the ratio of the input voltage to the output voltage.
Gain = Vout/Vin
The gain of this circuit is fixed by the resistors R1 and R2. Some of the output voltage is fed back to the inverting input. When an output signal is fed back to the inverting input of this type of amplifier we call it negative feedback.
Using negative feedback allows us to fix the gain of the amplifier. For this type of amplifier the gain is given by the following equation:
Gain = 1 + R1/R2
You have now provided all of the initial information required and the reader knows exactly what you are trying to accomplish
Having set up the circuit in Multisim we then proceeded to test it to prove that the gain of the circuit is given by Gain = 1 R1/R2.
From the circuit diagram R1 is shown as a 470 kΩ potentiometer set at 50%. This means that the value of R1 should = 235 kΩ. Therefore the gain of this amplifier should be:
Gain = 1 + 235/10 = 24.5
We simulated the circuit to show the input and output voltages on an oscilloscope. The reading of the oscilloscope is shown below.
Our simulated value is very close to the theoretical value. This method of measuring relies on exact placement of the cursors which is very difficult to do accurately. There is a better method known as AC analysis. This tests the voltage at a connection (node) over a large range of frequencies. We tested the output voltage a pin 6. Before we could do this we needed to know the node value of pin 6. We found this by double clicking it.
We then carried out an AC analysis on node 4. We set the vertical scale to decibels which is a special numbering system used in engineering to represent a large range of numbers over a small scale.
Finally we entered node 4 as the value to plot during the analysis.
We then carried out the AC analysis. We got the following readout.
Cursor 1 shows the value of the output where the line is flat(the upper graph). As the frequency increases we noticed that the output begins to become smaller. From earlier work we know that the bandwidth of a system extends up until the point that the output falls by -3dB.
Firstly though, we need to calculate the gain of the system. When the output is given in decibels the actual gain needs to be converted. This can be done using the following equation.
Gain(dB) = 20log (Vout/Vin)
The gain for this system is 27.78 dB. Therefore the equation can be manipulated:
(27.78)/(20) = log(Vout/Vin)
1.389 = log(Vout/Vin)
To get rid of the log on the Right Hand Side (RHS) we need to use the calculator. Press Shift>Log and enter 1.389. On your calculator it should look like this:
101.389 = 24.49
So the actual gain of the amplifier is 24.49 which is extremely close to the results predicted by theory.
Finally we were asked to work out the Gain Bandwidth Product of the amplifier. In order to do this we needed to find the bandwidth of the system.
The following screen dump shows how this is done. One cursor is set on the flat part of the output, the second cursor is carefully placed at the point where dy (the change in y) has fallen by -3dB.
X2 shows the frequency at which the gain has fallen by 3 dB. So the Gain Bandwidth Product for this amplifier is found by multiplying the gain by the bandwidth (the product).
Gain Bandwidth Product = 24.5 x 59,388
= 1.45 Mhz
The significance of the GBP is that we essentially have a trade-off. If we increase the gain we lower the bandwidth by the same proportion. If we increase the bandwidth we lower the gain by the same proportion. GBP is a very important operational amplifier parameter to know about.
Having completed the simulation we were required to build and test the circuit physically.
We began by building the circuit on breadboard. This is the initial circuit the variable resistor is set to 50% exactly as in the simulation.
This is the circuit with the power supply connections.
We then connected up the function generator and 2 channels of an oscilloscope. Channel A was used to measure the input and channel B was used to measure the output,
The oscilloscope was connected to a computer. Firstly we measured the input voltage using cursors placed as shown, the input voltage is given as dy (the change in y)
Because it is not very clear what the measurement is, we have zoomed in on the relevant part of the screen dump on the next slide where you can clearly see that dy is measured at 102 mV
We carried out exactly the same exercise for the output voltage.
We placed the cursors as shown and highlighted channel 2 (B). This gave us the correct reading for the output highlighted below.
The output is shown as 2.874 volts. So we can now calculate the gain:
Gain = 2.874/.103
Gain = 27.9
This is close to the reading we expected. The error is a result of component tolerances and the variable resistor not being set at exactly 50%. Indeed we can calculate the true value of the variable resistor as 27.9 = 1 + x/10:
X = 269 kΩ
Conclusion
I have learned many things during this exercise. Firstly I now know how to set up and test a non inverting amplifier which is very easy to use. I can use this amplifier in virtually any circuit I need in the future wherever I need to amplify an electrical signal. I have learned how to set the gain for this amplifier and how to measure it using a function generator and oscilloscope.
I know that negative feedback is used so that the gain of the amplifier can be predicted and that the gain of the amplifier is limited by its bandwidth (GBP). I have used new techniques such as AC analysis and the dB system to prove the gain of the circuit and also to calculate its Gain Bandwidth Product.