Parallel RLC Circuits - Help please

[edd83]

Homework Statement

I'm working through this question, but on the final part I've hit a brick wall so I'd be grateful for any help please.

The tuned circuit has a Q-factor of 1000 and is designed to resonate at 1MHz. At resonance, the supply current I is measured at 15μA for supply voltage of 2.5V. The load resistor, R_L is 10k ohms. The part of the question I'm not getting is:

Estimate the impedance offered to the supply at resonance and at the frequencies of + and - 2% from resonance

Homework Equations

I have also found that the bandwidth is 1kHz, at resonance the value of L is 25.33μH and the value of R is 0.162 ohms

The Attempt at a Solution

Could anyone suggest an equation? I'm stumped and can't think of what I need.

 

[Rellek]

Try calculating your complex impedance with the standard impedance equations for an inductor, resistor, and capacitor at the resonance frequency given. After finding the complex impedance in rectangular form, convert it to polar form and remember that current division still applies even when in the phasor realm.

For the +/- 2% part, just add and subtract 2% of your resonance frequency and recalculate.

 

[edd83]

Hi Relleck, thank you for your reply, I'll give that a try.

Forgive me for missing the bottom of the question off, is says 'use a 'narrow-band' approximation to find the impedance of the L-RC circuit'. Any idea what one of these is??

 

[ehild]

Hi Relleck, thank you for your reply, I'll give that a try.

Forgive me for missing the bottom of the question off, is says 'use a 'narrow-band' approximation to find the impedance of the L-RC circuit'. Any idea what one of these is??

I think it means that you can approximate the resonant angular frequency at ω₀≈1/√(LC), and Q≈(ω₀L)/R

ehild

 

[edd83]

Hi ehild, forgive me, how would I then go about finding the impedance?

 

[ehild]

The resonance frequency is given, and the Q factor too. You also know the voltage and current at resonance. From these, you can calculate the approximate values of L, R, C. You need the impedance of the whole circuit (between the terminals of the supply).ehild