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In this report, the design, construction, and characterization of various amplifier circuits used in circuit design are investigated. Non-inverting, inverting, and summing amplifier circuits are constructed, and their experimental output voltages measured to calculate experimental amplifier gain. The experimental gains of each were then compared to their theoretical values (except for the summing amplifier), and the accuracy of each amplifier was then estimated to help suggest suitable potential applications. Suggestions are made for sources of uncertainty.
The aim of this experiment is to determine the practical uses and limitations of various amplifier circuits.
The objectives of this experiment are:
Each amplifier circuit was made using the same prototyping board, consisting of 741 op-amp in open-loop configuration, the light-dependent resistor, and some resistors were never used.
+VCC, 0V, and -VCC were connected to the positive, ground, and negative terminals, respectively.
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+VCC and -VCC were connected to pins 7 and 4 of the op-amp. The power supply remained connected throughout the entire experiment but was turned off while circuits were not being analyzed. The power supply was set to supply 30V DC, with output potential split +15V and -15V relative to the ground 0V. Numbers on the diagram (Figure 4.) for the op-amp correspond to the standard 741 pin configuration.
An oscilloscope and signal generator were also used, with their grounds connected to the 0V terminal of the prototyping board.
The signal generator’s frequency and peak-to-peak voltage can be seen on the circuit diagram for each setup. The oscilloscope’s channel 1 was connected to signal generator output V In, and channel 2 to the op-amp's output VO so their voltage characteristics could be compared, and any anomalous performance be possible to observe. After the power supply was switched on for each experiment, the oscilloscope was auto adjusted. For all oscilloscope readings, a peak-to-peak voltage was measured to reduce the uncertainty in the experimental gain measured, although the peak voltage of the VO output is used in calculations (half the value). Readings of VO were recorded for each experimental setup, and oscilloscope graphs of both channels sketched with key values marked on the same graph. Key values included peak voltages and frequencies to check for a systematic error resulting from incorrect experimental setup. Experimental and theoretical gains were calculated, along with the percentage error after all experiments had been completed.
The non-inverting amplifier was set up according to Figure 1, with R1 = 1 kΩ and R2 = 10 kΩ. The signal generator was set to sinusoidal AC with a frequency of 1 kHz and a 2V peak-to-peak voltage. The result of VO was then recorded off the oscilloscope, and the experiment repeated with R1 = 10 kΩ.
The inverting amplifier was set up according to Figure 2, with R1 = 1 kΩ and R2 = 10 kΩ. The result of VO was then recorded off the oscilloscope, and the experiment repeated with R1 = 10 kΩ.
The summing amplifier was set up according to Figure 3, the oscilloscope was set to DC input coupling, to ensure the DC component of the output signal was not missed. For the cell, a standard AA battery was used at 1.5V.
Operational amplifiers are linear devices that have many uses in signal amplification and other applications such as conditioning, filtering, or other mathematical operations. Their operation is determined by external closed-loop feedback components used such as resistors that pass a small part of the output voltage back to the negative input, giving negative feedback, which forces the differential voltage between the input terminals to zero. A closed-loop gain is also developed far smaller than the open-loop configuration (which can be of the order of 10^5). This ensures higher stability as the voltage is amplified to within the range offered by the power supply. In all equations, V represents voltage at a certain point, R resistance of a component, and I the current in a branch, with all quantities being in SI units. Gain, G is a dimensionless ratio.
The experimental gain GExperimental is shown below in Equation 8, where VO and VIn are observed on the oscilloscope channels 2 and 1 respectively, peak-to-peak values should be used to reduce experimental uncertainty:
GExperimental = VO / VIn
Percentage error was calculated according to Equation 9:
Percentage Error = |GTheoretical - GExperimental| / GTheoretical × 100%
The inverting input is thought to be a summing point as the potentials from the negative feedback and the true input after passing through the input resistor R1. This resistor is required to separate the real input and inverting input. The non-inverting input is connected to earth, producing a virtual earth at the summing point and their voltage difference is forced to be zero. Using the facts that no current flows into the inputs and their voltages are equal and forced to zero, the closed-loop gain can be derived from first principles.
Current passing through both resistors can be thought of as being in series as none should theoretically enter the op-amp.
Current passing through both resistors can be thought of as being in series as none should theoretically enter the op-amp.
Equation 1. Current passing through Resistor network, with VIn being the voltage coming out of the AC power supply:
ITotal = VIn / (R1 + R2)
But as VVirtual Summing Point is forced to be zero, it can be assumed to be zero in Equation 2, this gives the theoretical ratio of VO / VIn, the closed-loop theoretical gain of the inverting amplifier, as seen in Equation 3 after rearrangement:
GTheoretical = -R2 / R1
The underlying theory of the non-inverting amplifier is the same as the inverting amplifier, except that VIn, the input voltage signal is applied to the non-inverting input terminal, giving a positive gain and an output signal in phase with the input. The negative feedback system to the inverting input is the same as with the inverting amplifier, forming a virtual summing point and equal potentials across the two inputs, the gain can then be theorized by treating the amplifier circuit as a potential divider, with VIn being a fraction of VO, with R2 in between the virtual summing point VIn and ground at 0V.
Equation 4.
VIn = (R1 / (R1 + R2)) * VO
Rearranging Equation 4 gives the ratio of VO / VIn, to get the gain of the non-inverting amplifier as seen in Equation 5:
GTheoretical = 1 + (R2 / R1)
The summing amplifier can be derived from the inverting amplifier, but with extra input R1 resistors in parallel with each other. This has the effect of making the output voltage proportional to the sum of the input voltages as seen in Equation 6. Where V1n and R1n correspond to the nth parallel input resistor, each fraction comes from Ohm's Law. The input voltages are from ground to the nth input resistor:
VIn = (R1 / (R1 + R1)) * V1n + (R1 / (R1 + R2)) * V2n + ... + (R1 / (R1 + Rn)) * Vnn
These can be substituted into the equation for the inverting amplifier (Equation 3) with ITotal equal to VIn / R1, this results in Equation 7 for the output voltage:
VO = -((R2 / R1) * (R1 / (R1 + R2))) * V1n - ((R2 / R1) * (R1 / (R1 + R2))) * V2n - ... - ((R2 / R1) * (R1 / (R1 + R2))) * Vnn
The results for each circuit configuration are shown below, and the sketched graph for the first resistor configuration of the non-inverting, inverting, and the configuration for the summing amplifier, figures 6 to 7 respectively. Each shows the observed oscilloscope output for the 2 connected channels with respect to the common ground connected to the power supply. The theoretical gains have been calculated using the derived equations for each experimental setup along with the percentage error in experimental gains. Peak-to-peak values as stated by the oscilloscope were used in calculations and to find peak graph values illustrated on figures 5 – 7 to reduce uncertainty in the calculations.
R1 = 1 kΩ and R2 = 10 kΩ
Channel 1 Input Peak = 1.0 V
Channel 2 Output Peak = 11.2 V
G Theory = 11.0
G Experimental = 11.2
% Error = 1.8%
R1 = 10 kΩ and R2 = 10 kΩ
Channel 1 Input Peak = 1.04 V
Channel 2 Output Peak = 2.08
G Theory = 2.0
G Experimental = 2.0
% Error = 0.0%
R1 = 1 kΩ and R2 = 10 kΩ
Channel 1 Input Peak = 0.96 V
Channel 2 Output Peak = 9.8 V
G Theory = -10.0
G Experimental = -10.2
% Error = 2.0%
R1 = 10 kΩ and R2 = 10 kΩ
Channel 1 Input Peak = 1.02 V
Channel 2 Output Peak = 1.04 V
G Theory = -1.0
G Experimental = -1.02
% Error = 2.0%
R1 = 1 kΩ and R2 = 10 kΩ
Channel 1 Input Peak = 0.92 V
Channel 2 Output Peaks = 8.5, -11.4 V
The summing amplifier output appears to match its output based off theory as seen in Equation 7.
All three amplifiers performed in a way that was expected of them, as their experimental gains were in line with their theoretical values. All percentage errors were under the 5% threshold suggesting the experiment was carried out in an accurate way and sources of error were minimal. Sources of discrepancy between theoretical and experimental values could be down to tolerances of the components such as resistors. Components may have also been non-ideal such as wires with non-zero resistance. The percentage error for the second amplifier circuit was zero, suggesting that an insufficient resolution was used on the oscilloscope, and that the equipment was limited. Human error in operating the equipment, measuring, and recording the results was not likely an issue due to the electrical equipment being entirely digital. All three graphs show a channel 2 output that was expected from theory, along with no observed frequency variation, suggesting the experiment was set up correctly.
Channel 1 peaks were not all 1 V, perhaps due to limitations in the signal generator and oscilloscope, but perhaps due to limitations in the ideal theory of op-amp operation, current may have flown into one of the inputs, and voltage difference between the two inputs may have been non-zero. This may have affected the experimental gains as well.
Modifying the resistor ratios successfully changed the gain value in line what was predicted from the theory on the non-inverting and inverting pairs of setups.
The operation of all three op-amp setups closely follows their underlying electrical theory; their gain and summing pattern followed what was expected of them. Despite their real-world limitations, they are suitable for use in many applications where reasonable accuracy is required, but extremely high accuracy is non-essential. Potential applications include audio amplification for use in sound systems or for the amplification of a weak electrical signal in a long wire. Gains could be adjusted using a variable resistor, enabling the fine-tuning of signal amplitude outside of a lab setting.
The summing amplifier demonstrated correct summing of multiple input signals. Uses for summing amplifiers include combining signals directly or scaling them as well with the use of resistors.
However, some applications may not be suitable due to the theory and operation of op-amps not being perfect; for example, essential medical equipment may need an alternative circuit or op-amp design before this particular op-amp model would be safe to use in such essential applications.
While the experiments produced results that closely matched theoretical expectations, it is essential to consider potential sources of uncertainty that may have affected the accuracy of the measurements:
Despite these potential sources of uncertainty, the experiments yielded results with percentage errors within an acceptable range, indicating that the overall accuracy of the measurements was satisfactory for the intended applications.
Based on the findings of this experiment, it is recommended that the amplifier circuits investigated can be used effectively in applications where moderate accuracy is sufficient. Some specific recommendations include:
However, caution should be exercised when considering these amplifier circuits for critical applications where extremely high accuracy and reliability are essential. In such cases, a thorough evaluation of the specific op-amp model and circuit design should be conducted to ensure suitability and safety.
Amplifier Circuit Experiment Report. (2024, Jan 06). Retrieved from https://studymoose.com/document/amplifier-circuit-experiment-report
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