1

The Tuned Circuit

Aim of the experiment Display of a decaying oscillation. Dependence of L, C and R.

Circuit

Equipment and components 1 Rastered socket panel

1 Resistor R1 = 10 Ω, 1 Resistor R2 = 1 kΩ

2 Capacitors C1, C2 = 0.1 µF

1 Capacitor Ck = 4.7 nF

1 Capacitor Cp = 10 nF

1 Coil, 500 turns, 1 Transformer core

1 Function generator

1 Oscilloscope

2 Sets of probes

Bridging plugs, Connecting leads

2

Conducting the experiment

Part 1 1. Assemble the measuring circuit.

2. Function generator: f = 100 Hz (square - wave)

U1 approx. 5 Vpp

Apply this signal to the differentiator (R2 C1).

At the output spike pulses will appear with positive leading and negative trailing

edges, which excite the tuned circuit.

Oscilloscope: Y1 (5 V/cm) first connected to the square-wave signal and then to the

spike signal.

Y2 (100 mV/cm) connected to the tuning circuit.

Time base: 1 ms/cm; AT

Coil without iron core. Short-circuit R1 = 10 Ω.

3. You should get the following graph. Make a true-to-scale drawing.

Part 2 4. Adjustments as in part 1, but slowly insert the core into the coil. Observe the

frequency

€

1T⎛

⎝ ⎜ ⎞

⎠ ⎟ of the decaying oscillation.

3

Part 3 5. Adjustments as in part 2, but connect a capacitor Cp = 10 nF in parallel to C2.

Part 4 6. Adjustments as in part 3, but remove the core, and also remove the short-

circuit across the resistor R1 = 10 Ω. When doing so, observe the decaying oscillation.

4

Parallel Resonant Circuit

Aim of the experiment Measuring the resonance frequency and displaying the resonance curve.

Changing the resonance frequency

Measuring the phase of the inductive and capacitive reactive current with respect to the resonance voltage

Measuring bandwidth and Q

Circuit

Equipment and components 1 Rastered socket panel

1 Resistor R1 = 10 Ω

1 Capacitor C = 0.1 µF

1 Capacitor Ck = 4.7 nF

1 Capacitor Cp = 10 nF

1 Coil, 500 turns, 1 Transformer core

1 Function generator, 1 Oscilloscope

2 Sets of probes

Bridging plugs, Connecting leads

5

Conducting the experiment

Part 1

1. Set U1 = 2 Vpp (sine). Measuring point A (Y1 :

€

1 Vcm

).

2. Assemble the circuit without the resistor R = 10 Ω (short circuit), and without

inserting the iron core into the coil.

3. Connect Y2 (

€

1 Vcm

, 10:1) to the point of Ck, L, C = measuring point B (‘hot’

point of the circuit).

4. Change the frequency until a voltage maximum is observed at Y2. Read off the

frequency.(This is the resonant frequency fres of the parallel-tuned circuit).

fres =

Ures =

Part 2.A

Measuring the resonant curve.

5. Connect Y1 (

€

200mVcm

) to measuring point B.

Set U1 to Ures = 1.2 Vpp (6 divisions.).

6. Measure the output for frequencies above and below the resonance frequency.

7. Tabulate the results and draw a graph.

In order to characterize a tuned circuit, those frequencies above and below the

resonance frequency are important where the voltage has dropped to:

€

Ures

2 = 0.707 Ures.

f/ kHz

U2/ Vpp

6

Part 2.B 8. Repeat the measurement with R = 10 Ω connected in series to the coil.

f/ kHz

U2/ Vpp

Make a diagram of both curves with U2 = Function of frequency F (f)

Exercise • Measure the band width (b), where b = 2 Δf

b =

• Measure the quality factor Q which is defined as the ratio between:

€

resonance frequencyband width

=f res2Δf

=Q

Q =

Part 3

9. Adjust the frequency of the generator to f = 5 kHz (2 Vpp).

10. Connect Y2 (

€

0.5 Vcm

, 10 : 1) to measuring point B and trigger on Y2.

11. Remove Y1. Slowly insert the iron core and see if a maximum can be

obtained:

Ures =

Part 4

12. Connect the capacitor Cp = 10 nF in parallel to the capacitor C = 0.1 µF and

retune the frequency for maximum:

fres =

Ures =

7

Series Resonant Circuit

Aim of the experiment Measure the course of the voltages across the resistor, the coil and the capacitor as a

function of the frequency

Measure bandwidth, and quality factor

Circuit

Equipment and components 1 Rastered socket panel

1 Resistor R = 10 Ω

1 Capacitor C = 0.1 µF

1 Coil, 500 turns, 1 Transformer core

1 Function generator, 1 Oscilloscope

2 Sets of probes

Bridging plugs, Connecting leads

8

Conducting the experiment • Measure the voltages across the resistor: UR.

• Measure the voltages across the capacitor: UC.

• Measure the voltages across the coil: UL.

With U1 = 2 Vpp

€

fkHz

€

UR

mVpp

€

UL

Vpp

€

UC

Vpp

Make a diagram of UR, UL and UC .

Exercises

• Calculate the band width b :

€

b = 2Δf =

• Calculate the quality factor Q :

€

Q =fres2Δf

=