Lab 13 - Bandwidth and Signal Analysis

Objective
- To understand how bandwidth is determined

Lab
For this lab, a RLC circuit is hooked up with a function generator to determine the bandwidth of the circuit.  Before measuring the actual bandwidth of the circuit, the theoretical values were calculated for two different circuits.  The two circuits use the same inductor value but have different resistors and capacitor values.
Components:
L = 1 mH
R = 100 Ω and  10Ω
C = 100 µF and 1µF

First Circuit

Resonance Frequency = 3162 rad/s

Quality = 0.032

Bandwidth = 98821

ITheoretical = Vm/sqrt(R^2 +(ωL - 1/ωC)^2) 

              = 3.47/sqrt(100^2+(3162*.001-1/(3162*100*10^-6))^2 

              = 34.7mA

IActual  =  34.1mA

Second Circuit

Resonance Frequency = 31622.78 rad/s

Quality = 3.16

Bandwidth = 10007.21 

ITheoretical = Vm/sqrt(R^2 +(ωL - 1/ωC)^2) 

              = 3.47/sqrt(100^2+(31622.78*.001-1/(31622.78*100*10^-6))^2 

              =  104.6 mA

IActual = N/A (did not get the image of the current at resonance frequency)

Comparing the two circuits, the angular frequency is smaller in the circuit with the 100Ω resistor and 100µF capacitor than the 10Ω resistor and  1µF capacitor.  This shows that at higher resistance and capacitance, the less frequency is needed to obtain resonance which results in a lower bandwidth.  From the lab, it shows that the lower the resistance and capacitance the higher the bandwidth.

Lab 12 - Low-Pass Filters & High-Pass Filters

Objective:
-Understand the purpose of Low-Pass filters and High-Pass filters in signal processing/modifications.

Lab:
For the lab, the theoretical gain for the low pass was first calculated.

The image above shows the calculations for the theoretical gain and a schematic of the circuit. 

The components that were used for the lab was a function generator, a 1000Ω resistor, and a 1µF capacitor.

The actual values for the 1000Ω resistor = 975Ω and the 1µF capacitor = 1µF.

The input voltage

Low-Pass Filter Results 

The gain is determined by dividing the Output voltage by the Input voltage. 

The results of the Low-Pass filter shows that as frequency increases, the voltage gain within the circuit will eventually reach zero .  

High-Pass Filter Result

The graph for the High-Pass filter shows a slight curve with the top of the curve being the natural response.  From the results, it can be determined that after the high-pass filter passes a certain frequency it begins to decreases.  The graph does not show past 10000 Hz due to the digital multimeter not being able to give good data at higher frequencies.