10.19.2021 -- The purpose of this lab is to build and test a bandpass filter. Fiters are used to filter addtional noise that may interfere with a signal. A bandpass filter is a "filter designed to transmit a particular band of electromagnetic frequencies while excluding those of higher or lower frequencies" (definition from https://www.wordnik.com/words/bandpass%20filter).
7.1 The Tank Circuit
Below in Figure 7.1 is the bandpass filter (or also termed the tank circuit) for the lab. Again, this tank circuit will only allow a certain range of frequencies through and any frequency lower or higher gets filtered out. THis circuit is tested in LTSpice and in lab. The equations needed to find frequencies and Q-points are listed in Figures 7.2 and 7.3.
Figure 7.1 The tank circuit for the bandpass filter
EXERCISE 7.1: Derive Equation 7.1 from the lab manual
Figure 7.2 Solution to Exercise 7.1
EXERCISE 7.2: Suppose L= 1 µH and RL= 1 kΩ for your tank circuit. Design the circuit to have a 600 kHz resonance frequency. What is the Q for this tank circuit?
Figure 7.3 Solution to Exercise 7.2
7.1a LTSpice Simulation
An LTSpice simulation is run on the tank circuit in Figure 7.4.
Figure 7.4 Tank circuit for LTSpice simulation
1)
Figure 7.5 Frequency, Q, and Vout calculations for Ex.1
2)
Figure 7.6 Voltage output for default tank circuit
3-5) Q increases as RL/RS increases.
Table 7.1 LTSpice AC Sweep Data
7.1b Assemble the Circuit
The circuit in Figure 7.4 is breadboarded, and the data is recorded in the Table below.
Lf1 | 10 µH | 10 µH |
Cf1 | 0.069 µH | 0.069 µH |
RL, RS | 100 Ω | 1 kΩ |
f res | 212.6 kHz | 214 kHz |
f low | 186.6 kHz | 202 kHz |
f high | 240 kHz | 224 kHz |
BW | 53.4 kHz | 22 kHz |
Q = f res/BW | 3.98127 | 9.72727 |
Table 7.2 Measurement AC Sweep Data
Conclusion
The data from Tables 7.1 and 7.2 do not match very close. However, the trend of the Q increasing as RL/RS increases still holds. Q is also known as the "resonant Q," and this defines the quality of the tank circuit.
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