Voltage Slope & Resonance Bandwidth (VSRB)

Objective

In order to:

• determine the resonant frequency based on the clamping voltage in a series LC resonant circuit
• measuring and determining the voltage drop in a series LC resonance circuit
• measure and determine upper and lower limits based on voltage gain
• using the voltage gain curve as a function of frequency 
• analyze and conclude about the comparison of voltage oscillation and amplification in series LC resonance circuits.

Basic Theory

LC Series Resonator Circuit

Information:

• VS = signal source voltage (v)
• VAC = LC circuit clamp voltage
• VAB = end voltage L
• VBC = end voltage C.

In a series LC resonance circuit, there is a voltage bounce at the ends of L and C against the clamping voltage with a voltage gain of VS/Vj or VL/Vj, where when resonance occurs, the voltage values ​​of VL and VC are maximum, so that the voltage gain value is also maximum, if the frequency given to the circuit is less or more than its resonant frequency, the voltage gain will decrease.

The upper limit frequency (f2) and lower limit (f1) values ​​can be determined when the input signal frequency is given to the circuit resulting in a voltage gain value reaching 70% of its maximum gain.

The width of the lane (B) can be determined by the calculation:

Calculating Frequency Bandwidth

Formula:

B = f2 - f1 atau B = fr/Qr dimana Qr = XL / RL

Information:

B = bandwidth (Hz)
f2 = upper limit frequency (Hz)
f1 = lower limit frequency (Hz)
fr = resonant frequency (Hz)
Qr = winding quality factor (times)
XL = inductive reactance (Ohm)
RL = pure resistance in the inductor at resonance (Ohm).

RF Amplifier

The utilization of voltage hopping is on the receiving antenna that captures the desired transmitter frequency. The L2 - C resonance circuit has a signal source from L2 itself, the result of induction from L1 which gets energy from the captured wave.

Work steps

1. Install the LC series resonance circuit on the work board
2. Give the AFG signal (2vp-p) at the circuit input.
3. Install the CRO (cathode ray oscilloscope) at the AC point (vj), then adjust the AFG (Arbitrary function generator) frequency until the amplitude at resonance is:
4. Fr = 62k Hz
5. Vj = 0.08 Vp-p
6. Without changing the AFG, measure the amplitude of point BC.
7. Fr = 62k Hz
8. Vc = 0.04 vp-p,

Based on steps 3 and 4 calculate:

1. Voltage gain = Vc/Vj = 0.04/0.08 = 0.5 times
2. Increase the AFG frequency setting, until the CRO shows an amplitude of 70% of the Vc voltage at resonance, Note!!
3. F2 = 93k Hz
4. 70% Vc = 0.028 Vp-p
5. Move CRO to point AC, note!!:
6. Vj x f2 = 0.1 vp-p (amplitude),

Based on steps 6 and 7 calculate:

1. Voltage gain when f2 = 0.28 times
2. Lower the AFC setting, until the CRO shows an amplitude of 70% of VC at resonance, note:
3. f1 = 56k Hz
4. 70% Vc = 0.028 vp-p
5. Move CRO to point AC, note the designation:
6. Vj*f1 = 0.06 vp-p (amplitude)
7. Based on steps 10 and 9, determine the voltage gain when f1 = 0.46 times.
8. Finished.