In the next sequence of posts the flat coil impedance characteristics are investigated using a range of different measurement methods. Understanding the flat coils impedance charactertistics with frequency is imperative if the coil is to be used optimally, and investigated accurately in experiments regarding the displacement and transference of electric power. Impedance measurements will establish a range of characteristic properties of the flat coil, including:

1. The fundamental resonant frequency of the secondary and the primary, their harmonics, and the effects of close coupling of the two coils.

2. The magnitude and phase of the impedance of the secondary and the primary, and their combination.

3. The effects of electrically loading the secondary and primary.

4. The effects of extending the conductor length of the secondary and primary.

5. Changes in the impedance characteristics when multiple flat coils are joined together.

6. Changes in the impedance characteristics when a flat coil is connected to earth.

7. Suggest bands of frequency that may prove interesting to experiment with the displacement and transference of electric power.

8. Indicate how best to match the flat coil to the required generator for maximum transfer of power.

9. Indicate how best to match the flat coil to the required load or experimental circuit.

The investigation of these characteristics are extensive and will be presented in several parts:

Part 1. Basic resistance and impedance characteristics of a single flat coil where the measurement is either made at dc and single spot frequencies using basic handheld type instruments such as a Digital Multimeter (DMM), LCR meter, and a dip meter.

Part2. Full impedance characteristics (magnitude and phase) with frequency of a single flat coil, measured using a Vector Network Analyser (VNA).

Part3. Full impedance characteristics (magnitude and phase) with frequency of flat coils coupled together in different experimental configurations, and again measured using a VNA.

The specific measurement equipment used in these parts include:

1. Low frequency spot measurements at 100Hz and 100kHz using a Eucol U822C handheld LCR meter (LCR).

2. DC resistance measurements using a UNI-T UT71E handheld DMM meter (DMM).

3. Dip meter measurements of the secondary using a Altai TR Dip Meter KDM-6 (DPM)

4. Impedance characteristics using an SDR Kits Vector Network Analyser 3E (VNA-SDR). This VNA has been used for most measurements as it provides data directly connected to a computer, and hence can be more easily displayed and analysed.

5. Impedance frequency scans using a Hewlett Packard 4195A Network Analyser (VNA-HP) mainly to check and confirm the accuracy of the results obtained with the VNA-SDR, and also to use the equivalent circuit function to model actual device circuit equivalent values.

6. Frequency accuracy scans to check the frequencies generated by the DPM, or any other oscillators required, using a Tektronix 7L5 low-frequency spectrum analyser mounted in a Tektronix 7854 mainframe (SPA-TEK).

Each instrument was first calibrated accordingly and tested on a known impedance load or frequency standard in order to confirm accurate measurement. Connection leads were kept short and minimal, and where possible their effects removed by the calibration procedure. At the end of a measurement period the calibration of the instrument was again checked on the same known impedance to confirm stable calibration and measurement.

In this first part the flat coils 3S-1P, and 1S-3P were used. The 3S-1P flat coil has a removable secondary allowing for independent secondary and primary measurements as well as combined, whereas 1S-3P has a fixed secondary and primary.

**LCR/DMM Measurements**

Figures 1. below show a summary of the measurements made using the LCR and DMM, and the full data is summarised further below.

LCR/DMM Measurements for 3S-1P Primary
Inductance L: 6.453µH @100kc/s Impedance Z: 4.055Ω @100kc/s Resistance R: 0.00131Ω @100c/s DC Resistance R: 0.00Ω
Inductance L: 6.485µH @100kc/s Impedance Z: 4.074Ω @100kc/s Resistance R: 0.00145Ω @100c/s DC Resistance R: 0.00Ω |
LCR/DMM Measurements for 3S-1P Secondary
Inductance L: 290.98µH @100kc/s Impedance Z: 182.82Ω @100kc/s Resistance R: 0.5758Ω @100c/s DC Resistance R: 0.70Ω
Inductance L: 290.41µH @100kc/s Impedance Z: 182.46Ω @100kc/s Resistance R: 0.5537Ω @100c/s DC Resistance R: 0.80Ω |

LCR/DMM Measurements for 1S-3P Primary
Inductance L: 5.097µH @100kc/s Impedance Z: 3.223Ω @100kc/s Resistance R: 0.00098Ω @100c/s DC Resistance R: 0.00Ω |
LCR/DMM Measurements for 1S-3P Secondary
Inductance L: 298.36µH @100kc/s Impedance Z: 187.47Ω @100kc/s Resistance R: 0.5475Ω @100c/s DC Resistance R: 0.45Ω |

**Summary of the LCR/DMM results and conclusions so far:**

1. The secondary inductance indicated from the flat spiral coil calculator in Part 1 of the design was (2 x 71.419µH for an upper and lower coil) = 142.84µH. From the basic spot measurements we find that the actual inductance of the secondary is almost double for both types of coils 1S (298.36µH) and 3S (290.98µH). The coil calculator assumes a solid conductor, and is also not designed to account for the specialised inter-leaving that has been used to construct the upper and lower turns of the secondary. It is also unclear what model the calculator is using to calculate inductance for the spiral conductor. It is concluded that the flat spiral coil calculator is useful for the mechanical design of the secondary but not in predicting the inductance of the coil for an inter-leaved secondary in this case.

2. The primary inductance indicated from the flat spiral coil calculator in Part 3 of the design was 4.811µH. From the basic spot measurements we find that the actual inductance of the 3P primary (copper strip) is closer to that predicted at 5.097µH (+5.9% error) showing that the coil calculator can more accurately calculate the inductance in a simple case of a small number of turns with a solid conductor. In the case of 1P primary (silicone coated micro-stranded cable) again the conditions are more difficult and the inductance increases away from that expected from the design, measuring 6.453µH (+34.1%). It is concluded that the flat spiral coil calculator is useful for the mechanical design of the secondary but not in predicting the inductance of the coil for complex cable materials and geometry.

3. The slight decrease in inductance and impedance of the 3S secondary when added to the 1P primary to make the 3S-1P flat coil indicates a loose coupling between the two coils of < 0.25, which is best suited to establishing a resonant cavity in the secondary, and hence to experiments in to the displacement and transference of electric power.

4. The impedance and resistance of the primary in both cases 1P and 3P is low, and hence suitable for the generator to pass large oscillating and transient currents which will be needed to drive the flat coil in the intended experiments.

5. The magnitudes of inductance, impedance, and resistance of the secondary and primary appear to be generally in the correct region for the intended experiments. A clearer view of the frequency characteristics and impedance matching requirements will be established in part 2.

**DPM Measurements**

For dip meter measurements a 180cm lead was added to the outer or bottom-end coil terminal in order to lower the impedance sufficiently for λ/4 measurements. As the dial of the dip-meter is not a very accurate scale the oscillator setting was checked for frequency using the Tektronix 7L5 spectrum analyser with a small pick-up antenna.

For 3S-1P results a short telescopic aerial fully retracted 15cm long was added to the central coil terminal, which is to allow for fine wire length tuning during telluric reception experiments.

For 1S-3P results a ceramic bulb holder and a neon bulb was added to the central coil terminal, which will be used in experiments in the displacement and transference of electric power.

Figures 2. below show a summary of the measurements made using the DPM, and the full data is summarised further below.

DPM Measurements for 3S-1P Secondary
Frequency of dip meter maximum: 2625kc/s
Frequency of dip meter maximum: 2605kc/s |
DPM Measurements for 3S-1P Secondary
Frequency of dip meter maximum: 2730kc/s |

**Summary of the DPM results and conclusions so far:**

1. The frequency at which a 180° phase change due to the λ/4 wire length was designed at 2400kc/s in part 1 of the design. In the dip-meter measurement the coil is very loosely coupled to the meter, and so the secondary is very lightly loaded where the point of maximum impedance of the parallel resonant circuit will occur very close to the 180° phase change. The results of 2625kc/s for 3S and 2730kc/s for 1S are higher than expected from the simple calculation from wire length in part 1 of the design, but may also indicate other influences on the fundamental resonant frequency such as the inter-winding capacitive network of the coil.

2. The effect of the 3S added to 1P to form the 3S-1P flat coil shows a slight loading from the primary on the secondary and hence reducing the resonant frequency from 2625kc/s to 2605kc/s. This is again indicative of a loosely coupled coil suitable for the intended experiments.

3. It was not possible to identify any harmonic resonant frequencies above the fundamental using the DPM. It is most likely that the harmonics are much smaller in amplitude than the fundamental, and that the method of tuning the DPM is not sufficiently sensitive to detect and indicate the very small harmonic changes.

4. The basic frequency points derived from the DPM are generally in the correct region for the intended experiments. A much clearer view of the frequency characteristics will be established in part 2.

Click here to continue to the flat coil frequency measurements part 2.