H4_Noor_Alam

pdf

School

McMaster University *

*We aren’t endorsed by this school

Course

2E04

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by AmbassadorRedPanda3313

Noor Alam 400244448 Eng Phys 2E04 - Deliverable 4 Filters The circuit after the components were measured with the Hantek oscilloscope This lab is based on building a filter circuit using an AC electric circuit that is capable of passing or amplifying certain frequencies while attenuating other frequencies.Thus, a filter can extract important frequencies from signals that also contain undesirable or irrelevant frequencies. The circuit I am going to build for this lab will consist of an AC signal generator connected to a capacitor and a resistor in series and to a network of imperfect inductor (which has an internal resistance) and resistor. The node above R3 in the circuit is going to be the V output of the circuit. Through this circuit, I will determine its transfer function through analytical procedure and determine the type of filter, the circuit’s central frequency and -3dB frequency through analytical procedure and physical measurement, hence compare these values.

Analytical Solutions The calculation is performed in maple These variables were declared before the calculations are performed. SInce the value of frequency will vary, while calculating omega - the value of f is not declared As we are dealing with AC circuit, the impedance of the capacitor and the inductor and measured using the formula Hence :- The total impedance of the inductor and the resistor R2 in parallel are measured using the formula of effective resistors in parallel formula

The transfer function, H(f), is the ratio of the output voltage to the input voltage. This is also the ratio of output impedance to the total impedance. H(f) = Gain = V o (f) / V in (f) = Z par /(Z par +Z C +R1) The transfer function Using maple, I can plug the values of the variables in the transfer function and the value is :-

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Filter Type Through inspection, I can predict the kind of filter my circuit would be. At a very low frequency, the capacitor will act as an open circuit. This is because at a very low frequency, the impedance approaches to infinite. As omega approaches 0, Z C approaches ∞ And at a very high frequency, the inductor will act as an open circuit and the capacitor will act as a short circuit. The capacitor will act as a short circuit because the impedance will appeach a value of 0, while the inductor's impedance as seen in the formula will Approach a value of ∞. From the transfer function equation, we can determine that as f approaches ∞ in H(f) the numerator is close to 0. And when the value of f approaches to a very high value, ∞, H(f) = 0.910. lim f →∞ Hz As the capacitor and the inductor are not connected in series but in parallel and the values deduced from the analytical procedure and the limit calculation, the circuit built is a High-pass filter. Plotting the graph of the transfer function with respect to varying frequencies, it is evident that the filter is High-pass. At a very low frequency, the corresponding value of the transfer function or the gain is close to 0. And as the value of frequency gradually increases, the value of gain simultaneously rises, until it reaches the limit where V output is equal to V input Therefore this is a high pass filter.

Center frequency The center frequency, a term used for the frequency at which the gain in the transfer function reaches its maximum value. As it is a high pass filter, we have to raise the value of frequency to a very large value, and that is infinity - ∞. Using maple, I can derive the value of |H max | from the plotted graph. The value of |H max | when converted to dB is :- 20*log 10 (0.908019936) ≈ -0.838 dB -3dB frequency -3dB frequency is also known as the cut off frequency. This corresponds to the input frequency that causes the output signal to drop by -3dB relative to the input signal. The outpower is reduced by one-half or |H max |/sqrt(2). The cutoff frequency calculated from the maple software is :- The cut-off frequency is 2180 Hz. The phase diagram

This code is utilized to form the graph of the phase diagram. This diagram will be used as a comparison towards the end of this report. The phase diagram displays how the phase of the output voltage changes with respect to the input voltage from the power supply as the frequency varies across the circuit. Multisim Soluton I have inspected my circuit in the multisim software and obtained the following results:- Variables Values Center Frequency ∞ Hz |H max | 0.9080199366 |H max |/sqrt(2) 0.6420670546 -3dB Frequency 2180 Hz

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Using the AC sweep function in the multisim software, it automatically generates a suitable graph of the Magnitude of gain vs the frequency of the AC signal generator. The cursor is used to find the gain at certain frequencies for the sake of this lab. The ranges of the axis were adjusted to a suitable degree. The curser (2) is moved across the graph. In order to obtain the value of center frequency , the cursor is moved to the right end of the graph. The corresponding gain for the frequency is 908.0199*10^-3 as displayed for the value of y2. As the |H max | value is 0.9080199, 1/sqrt(2) of its value is equal to 0.64207. But trying to approach as close to this value using the cursor, the -3dB frequency is determined to be 2201 Hz.

The acquired value from the multisim software is compared in the above tabulated table. Since the center of frequency is ∞ Hz, there is no percentage difference that can be calculated for this variable. However, the value for |H max | in multisim is the exact value that was determined analytically. This indicates that the analytical procedure is correct. From the method used to attain the value of -3dB frequency, there is only ≈ 1% percent difference between the analytical and the multisim values. The phase diagram that is built in multisim is :- This graph will be utilisez at the end of the reason for comparison. Variable Analytical Multisim Center Frequency ∞ Hz ∞ Hz |H max | 0.9080199366 0.9080199 |H max |/sqrt(2) 0.6420670546 0.642067 -3dB Frequency 2180 Hz ≈ 2201 Hz

Physical Measurement The figure displays the circuit that the designed circuit set up on the breadboard and has each of the components labeled.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

In order to set up the circuit, I have connected the AC signal generator at 2.5Vpk to this breadboard circuit using the hantek oscilloscope. I have tried to set up my circuit on the breadboard just like the intended circuit designed in the multisim software. I employed jumper wires to connect the components that are in parallel to the capacitor and the power supply. The jumper wires were also used to connect the probes to the necessary places to attain the graphs of V in and V output in the Hantek Oscilloscope. To find the center frequency and -3db frequency and their gains, I will be proceeding in this section of the lab by taking various values of frequencies and their corresponding value of gain.

Frequency = 5000Hz Gain = (2.32+1.84)/(2.56+2.36) = 0.845528 Phase diff = 19.6*10^-6 * 5000 * 360 = 35.28 deg -3dB Frequency Frequency = 2180Hz Gain = (1.60+1.44)/(2.56+2.40) = 0.6129 Phase diff = 104*10^-6 * 2180 * 360 = 81.62 deg Frequency = 1000Hz Gain = (580+360)*10^-3/(2.64+2.48) = 0.1850 Phase diff = 136*10^-6 * 1000 * 360 = 48.96 deg

The tabulated values below have been attained using the same calculation method as the ones performed above. The tabulated values are then used to plot a graph of Gain vs Frequency and Phase vs Frequency, where the frequency is in logarithmic scale, for both the graph. Frequency (Hz) Phase (deg) Gain 10 29.376 0.016 100 104.4 0.017 500 64.8 0.063 1000 48.96 0.185 2180 81.7 0.613 5k 35.28 0.801 10k 23.76 0.918 50k 10.8 0.929 100k 5.76 0.927 500k 0 0.934 1M 0 0.976

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

The value of |H max | as frequency increased to a vast amount, the value of gain approached a value of approx. 0.93. I input the -3dB frequency (2180 Hz) in the Hantek Oscilloscope and it led me to determine a gain value of 0.613. The phase diagram, although the majority of the plotted graph followed the trend as displayed in analytical and multisim, I discovered an anomaly. For the value of -3dB frequency,the corresponding value of phase is out of place. This could have occurred due to errors carried forward while measuring using the cursor in the hantek oscilloscope or other reasons such as the uncertainties in this lab. Since we are working with an AC electric circuit, the values in the oscilloscope fluctuated between the range 15-25 mV, which made it difficult to record a value sometimes. The scale of volt/div of each channel are different for each measurement of frequency, as I had to adjust it to a suitable degree to attain as accurate and precise value as possible. However according to the hantek manual there is a 土 50mV uncertainty in the measurement of voltage. For phase difference between the waveforms with respect to V in or Channel 1, the scale in the oscilloscope was set to varying degree automatically or manually for measurement purposes. The oscilloscope indicates that it illustrates a 土 0.5 μs uncertainty, when measuring the time difference. A number of other uncertainties were also taken into account that could have led to the unfortunate event of the ammeter, such as DMM in the hantek has an uncertainty of (1.3% +2) for AC current measurement. The value of inductance in our measurement could not be

measured as I did not have the necessary equipment, however the internal resistance of the inductor was measured to be approximately 220 Ω. The resistors have a tolerance of 1%, the capacitors have an uncertainty of (3% + 5). These various sources could have been the causes of the undetermined value of current across the inductor I L . Analysis Since the values of analytical and multisim values are barely the same with only approx 1% percentage difference between the value of -3dB Frequency. I will proceed to compare the values of analytical and the physical measurement solutions. For the value |H max | has only 2.4 % percentage error while the |H max |/sqrt(2) value has a percentage error of 4.5%. The values are fairly similar, although this lab had us deal with AC circuits and the several uncertainties of the hantek oscilloscopes and probes. Variable Physical measurement Center Frequency ∞ Hz |H max | 0.93 |H max |/sqrt(2) 0.613 -3dB Frequency 2180 Hz Variable Analytical Multisim Physical measurement Center Frequency ∞ Hz ∞ Hz ∞ Hz |H max | 0.9080199366 0.9080199 0.93 |H max |/sqrt(2) 0.6420670546 0.642067 0.613 -3dB Frequency 2180 Hz ≈ 2201 Hz 2180 Hz

Phase diagram Analytical Multisim Physical

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

From the look of the above diagrams, the phase diagrams in all the 3 solutions follow the same trend. Where the phase difference attains a minimum value at very high frequency, this is because V out becomes close to V in and there is a very large difference in phase at low frequencies. The gain of this high pass filter is very low in low frequencies and extremely high in high frequencies. The only misshapen in this diagram is that the phase difference for the -3dB frequency does not follow the trend. This could be due to the difficulty faced while calculating the time difference between the waveforms. Reflection In this lab, I have learnt how different arrangements of the components - capacitors and inductors of different magnitude can be used to create different kinds of filter. High-pass, Low-pass, Notch filter and bandpass filter. Although it was fun to determine and calculate the transfer function for different ranges of frequencies, it was nonetheless a meandering process as a small mistake could lead to numerous changes and large errors. Filters are used in several real life applications so that generators can only attain certain frequencies of signal and not function under unnecessary circumstances. This operation is used in wind turbines, that often utilizes bandpass filters. The turbines perform this so that it can generate constant power output and prevent the turbine from being damaged