Measurements in Radio Engineering

Lab01-Mutual Inductance Measurement

1. Motivation

- Wireless charging

- Wireless power transfer for implanted devices

- NFC/RFID

2. Theory

Two coils placed close to each other can be represented by the following circuit.

2.1 Inductance Only Measurements

From the basic circuit theory, we can write

(1)

(2)

With , we obtain

Measure the primary coil inductance using an LCR meter with the secondary coil open-circuited to obtain L₁₁.

(3)

Similarly measure the secondary coil inductance with the primary coil open-circuited to obtain L₂₂.

(4)

With the secondary coil shored, we have

(5)

Use (5) in (1) to obtain

(6)

From (6)

(7)

(8)

Quality factor:

(9)

2.2 Inductance and Resistance Measurements

(11)

(12)

(13)

(14)

With the secondary circuit shorted:

(15)

(16)

3. Measurements

3.1 Two identical coils with zero coil gap

f = 100kHz

Use a series equivalent circuit for the inductance measurement.

Use L, Q measurement

1) Measure L11 and Q11.

2) Measure L₂₂ and Q₂₂.

3) Measure L_11s and Q_11s.

4) Find k.

5) Find M.

3.2 Repeat 1 with 3-mm coil gap.

4. Sample Results

- Use 'COUPLED COIL ANALYSIS'

- Coils used: 2 units of Abracon LLC AWCCA-50N50H35-C01-B

Figure: Materials for mutual inductance measurements. Two 100-kHz inductive charging coils (Abracon LLC AWCCA-50N50H35-C01-B), a 3-mm thick spacer, a paper clamp for short-circuiting the secondary coil

- Coil gap = 0mm

* Measurements: 100kHz, Ls-Q, Keysight E4980A LCR meter (20Hz-2MHz)

L11, Q11: 46.6uH, 188

L22, Q22: 46.6uH, 188

L11s, Q11s: 7.53uH, 27

* Calculation:

R11, R22 (ohms): 0.156, 0.156

k = (0.916, 0.0028)

Rm, Lm, Qm: 0.061, 42.7uH, 442

- Coil gap = 3mm

L11, Q11: 33.2uH, 184

L22, Q22: 33.2uH, 184

L11s, Q11s: 15.8uH, 72

* Calculation

R11, R22 (ohms): 0.113, 0.113

k = (0.724, 0.0028)

Rm, Lm, Qm: 0.024, 24.0uH, 626