If we want to select a signal from a mess of interfering signals, and if the des

Question

If we want to select a signal from a mess of interfering signals, and if the desired signal is confined to a narrow range of frequencies, we can often use a resonant circuit: For example, if we want to select a station in the FM broadcast band (88.1 MHz to 107.9 MHz in the U.S.) we might choose to have an inductance of L=0.13uH. Assume that the input resistance of the first stage of the receiver is R=2Kohm. What is the appropriate capacitance for the variable capacitor to select the station at f=97.7 MHz? Express your answer in picoFarads. What is the Q of the system for the capacitance that selects the station at f=97.7 MHz? What is the bandwidth of the system for the capacitance that selects the station at f=97.7 MHz, in MegaHertz? A wizardly engineer suggests that we could use an active circuit to enhance the Q of the tuned circuit and thus increase the selectivity, as follows: The active circuit the engineer suggested was the following: Assume that the operational amplifier is ideal. In the space provided below give an algebraic expression for the equivalent resistance v/i of this circuit as seen from the indicated port, in terms of the resistances in the circuit diagram. Which of the following phrases best describes this circuit? (a) resistance multiplier, (b) negative resistance, (c) oscillator, (d) amplifier, (e) none of the above. If we fix R1=R3=2700 ohm, what should we make R2, in Ohms, to make the Q of our tuned circuit 100 at our station f=97.7 MHz?

Explanation / Answer

Please ask if you have any doubt.I will help you.

1) C = 1 / (42 L f2 ) = 20.41 pF

2) Q = R (C/L) = 25.06

3) Q = o / ,where is bandwidth ,

o = 97.7 MHz gives

= 3.89864 MHz

4) The given op amp answer is : b) negative resistance .

The effective Rin of the given op amp is

Rin = - R2 (R1 / R3)

As given R1 = R3 , therefore

Rin = - R2 .

Now this is placed in parallel with R.

Reff = R(-R2) / (R - R2) .

Thus Reff will be in parallel with L & C.

Now we want Q' = 100 and we need to find R2 for it.

Q' = Reff (C/L) gives Reff = 7980.87

Thus , (2000)(-R2) / (2000 - R2) = 7980.87 gives

R2 = 2668.8 .

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