Inverting amplifier - Essay Example

Inverting amplifier a. b. The requirements for the circuit specify a negative voltage gain. To achieve such a gain, an op-amp may be used as an inverting amplifier. With such a design, the gain can then simply be computed as: However, it should be noted that the transducer itself has variable impedance. Due to this internal source impedance, the gain of the circuit may vary. It is therefore important that the circuit be designed to satisfy certain variation requirements. For the given circuit, a tolerance of 10% is given for the gain. This results to the following minimum and maximum gain values: Due to the effect of the source impedance, the gain equation for the inverting amplifier has to be modified to include a series resistance. The resulting equation is given below: Since the feedback and input resistances are constant, the gain variation is dependent solely on the source impedance. It then becomes apparent that maximum gain is achieved only when the source impedance is at a minimum value (assumed to be zero). Likewise, the minimum gain is reached when the source impedance is at a maximum value of 50 ohms. Using this information, the following equations are constructed: Rearranging the variables, the following system of linear equations is derived: Solving these equations, the values for the feedback and input impedances are obtained: c. The designed circuit was simulated using Multisim. To determine the gain characteristics at the minimum and maximum source impedance settings, two sets of simulations were run. The first set was performed with a source impedance of 50 ohms and the second set shorted the said resistor. To more effectively capture the response of the circuit, a DC sweep was performed from 100 mV to 1V for each simulation. The results of the simulations can be seen below: Seeing these results, it can be said that the actual response of the circuit was above the lower limit for the gain. However, under certain conditions, it can be seen that the actual response of the circuit exceeds that of the theoretical upper boundary established. This difference is present due to the fact that the design took into consideration an ideal op-amp while Multisim uses a more complex model. Particularly, the finite input resistance and the presence of offset voltages may explain the variations from the design. d. A basic op-amp may be used for this circuit. To reduce the effect of input resistance, a low offset JFET input op-amp such as the LF411 may be appropriate. The resistors for the circuit have the values shown in the circuit above. 1. a. To analyze the given circuit, it is useful to treat the op-amp as an ideal device with infinite input impedance. Knowing this, it is easy to derive the output expression for the circuit. Using the principle of superposition, the effect of each source can be taken while the remaining sources are shorted to ground. For instance, the effect of v1 on the output can be treated separately while v2, v3, and v4 are connected to ground. Due to the infinite resistance of the op-amp, the following equation can be obtained: Since the potential on the inverting and non-inverting inputs of an op-amp can be seen as equal the non-inverting input can be seen acting as a virtual ground. Knowing this, the previous equation can be transformed using Ohm’s law to: This equation can be subsequently transformed into: Using a similar analysis, the remaining contributions to the output voltage are obtained: Taking the sum results to the output voltage expression: b. Assuming values of 1k, 2k, 3k, and 4k for R1, R2, R3, and R4 respectively and a value of 2k for the feedback resistor, the following output voltage is obtained: c. The circuit was simulated on Multisim with the following circuit: Using this schematic, a value of 799.979 mV was obtained at the output. Comparing this to the theoretical output voltage reveals that the circuit operates close to ideal. The remaining error can again be attributed to imperfections of the devices. d. For a single op-amp device, the LM741 is a practical choice with the option to compensate for offsets. The resistors used for the circuit can be any resistor with the given values. 2. a. Instead of analyzing the given circuit from the most basic principles, it is more efficient to take into consideration that this circuit is constructed using the previous circuit. With the ideal zero-ohm output resistance and infinite input resistance, the two op-amps can be treated as independent circuits. The output of the first op-amp is simply a voltage source for the next op-amp. This analysis results to the following two equations: Combining and simplifying these equations leads to the expression: b. Substituting the given values into the equation leads to the following solution: c. The circuit for simulation in Multisim is shown below: Based on the given schematic, a value of 488.858 mV was obtained at the output. This is close to the 500 mV theoretical value. The discrepancy may again be associated with the non-ideal response of the op-amp model used in Multisim. d. As two op-amps are used for this circuit, a dual op-amp chip may be utilized for a more compact circuit. For a circuit where accuracy is not critical, the LM358 can serve as a good option. Again, the resistors are of the given values in the circuit. 3. a. Since the coupling between the primary and secondary coils is ideal, the voltage at the output can be computed from the turns ratio. For an input of 220 Vrms, this is shown below: b. The peak voltage across the secondary winding is directly computed from the rms value as shown: c. The turns ratio equation is also used to determine the instantaneous voltage: d. The transformer circuit can be simulated in Multisim using the given schematic: The resulting response is modelled using transient analysis as shown below. Note that the primary signal is graphed in green while the secondary is shown in red. Extracting information from this graph, it can be seen that the value of the output when the input is at its peak (220 Vrms) is 6980.4 Vpk or 4935.89 Vrms. These values are again close to the theoretical estimates. At the 40V point of the input, the output is exactly at 900V which is identical to the theoretical value. Read More