Flat Coil Impedance – Part 3

This part measures the impedance characteristics Z11 (magnitude and phase) for the flat coil in a range of different experimental scenarios. There are some preliminary results presented here in order to give an indication of the more complex frequency characteristics that exist within the experimental scenarios. The measurements and explanantion of the results presented here is still work in process and hence this post has not been fully finished at this time. As soon as time allows I will extend the range of measurements and experiments, and provide more detailed explanations and implications of the presented results. The impedance characteristics reported so far currently relate to the following experiments:

1. Two flat coils bottom-end connected via a load and being used for experiments in the displacement and transference of electric power.

2. Two flat coils bottom-end connected to the earth with ground rods and separated in distance by 250m being used for experiments in the telluric displacement and transference of electric power,  (the generator flat coil in the lab, and the reception flat coil in the surrounding forest).

The details of these experiments will be reported in their own posts, although some pictures of the experimental arrangements are provided here for clarity, along with the preliminary impedance characteristics measured in those experiments.

Figures 1. show the experimental arrangements being used:

Figures 2. show the impedance characteristics measured for these experimental arrangements:

Note: this post is to be completed to include a more comprehensive set of impedance characteristics for the full range of experiments undertaken, along with their consideration, explanation, and implication to the purpose of the overall experiments.

Click here to continue to the flat coil single wire currents experiment part 1.

 

Flat Coil Impedance – Part 2

In this second part full input, small signal, impedance characteristics Z11 (magnitude and phase) with frequency of a single flat coil are measured using a Vector Nework Analyser (VNA). The SDR-Kits Vector Network Analyser 3E (VNA-SDR) is predominantly used as it provides data directly connected to a computer. Some measurements have also been cross-measured and checked using a Hewlett Packard 4195A Network Analyser (VNA-HP), and particularly when an  equivalent circuit function is required to model actual device circuit equivalent values.

The measurements reported in this second part are for Z11, the effective input impedance that the generator will see when connected to the input of the flat coil, and subsequently in part 3 connected  with a range of loads and other flat coils. Impedance measurements for Z21 the transmission impedance between the input of the primary and the output of the secondary will be reported in future parts.

For network analyser impedance-frequency measurements an adjustable capacitance box was connected across the primary coil at the correct termination point to match the equal weights of copper for the secondary and primary. The unconnected load capacitance of the box when set to 0pF is 30.5pF. The VNA being used was calibrated to the end of the coaxial cable to be connected to the capacitance box and then tested with a 50Ω termination for accuracy over the frequency range. This calibration was then re-checked at the end of the measurement cycle to confirm stable calibration throughout the measurement period.

A wider band frequency scan 0.1MHz – 20MHz was used initially in order to identify the fundamental resonance frequency, any low-order harmonics, and any other impedance features of interest. Subsequently the frequency scan band was reduced to (0.1MHz – 5MHz) to allow for greater detail in the results.

Figures 1. show the measurement arrangement.

VNA-SDR Measurements for 1P Primary

Figures 2. show the wide frequency scan VNA impedance results for Z11 from calibration and through changing load capacitance on the primary. It is recommended to view the full-size scan images where the detail can be seen much clearer, (click on the image to see the full-size image and navigation icons). Below the figures 2. each individual result is considered and explained. In the explanations standard abbreviations are used as follows:

LP = Inductance of the primary coil.

CP = Capacitance box value connected in parallel with the primary coil.

LPCP = Parallel resonant circuit formed by the primary.

CPP = Self-capacitance of the primary including the parasitic capacitance of the capacitance box when set at 0pF, which in total has been measured to be 30.5pF.

FP = Fundamental resonant frequency of the primary.

LS = Inductance of the secondary coil.

CS = Self-capacitance of the secondary coil.

LSCS = Resonant circuit formed by the inductance of the secondary combined with self-capacitance of the secondary.

FS = Fundamental resonant frequency of the secondary (FS1).

FS2 = Second harmonic of FS up to FSN the nth-harmonic.

FØ = Frequency at which a phase change takes place.

FØ180 = Frequency at which a 180° phase change takes place.

FU = Upper resonant frequency of the flat coil.

FL = Lower resonant frequency of the flat coil.

M1 – MN = Frequency markers on the results can be identified with a down pointing arrow on the result curve with a number above it.

Q – The quality factor of an impedance feature. For example, as the Q increases a resonance peak will become sharper and narrower, and as the Q decreases a resonance peak will become more rounded and wider.

|Z| – Magnitude of the impedance, (|ZS| for secondary, |ZP| for primary, |ZU| for the upper frequency of the flat coil, and |ZL| for the lower frequency of the flat coil).

Ø – Phase of the impedance.

To view the large images in a new window whilst reading the explanations click on the figure numbers below:

Fig 2.1. Shows the calibration to the end of the bnc connected to the primary capacitance box (CP). For this calibration the bnc was terminated with a standard 50Ω load and can be seen to be constant over the calibrated range of 0.1Mc/s and 20Mc/s. The phase in the calibration will swing repeatedly between ±180° indicating the near perfect match between the output impedance of the VNA (50Ω) and the standard 50Ω termination, as expected for a calibration of this type of instrument. M1 confirms the impedance magnitude 50.00Ω and phase -1.19° at 2863kc/s.

Fig 2.2. Shows the 1P primary with CP=0pF (30.5pF from the self-capacitance of the primary turns and parasitic capacitance combined, CPP). There is a strong parallel self-resonance of the primary coil which results from combination LPCP. From marker M1 the fundamental resonant frequency FP=9718kc/s with the 180° phase change, characteristic of a resonant circuit, shifted to a much higher frequency above the upper limit of the scan (20Mc/s). The large shift between FØ180 and FP results from the large imbalance between the inductance of the coil LP and the very small self-capacitance CP . As CP starts to rise in the following figures FØ180 will start to fall in frequency.

Fig 2.3. Shows the effect of increasing CP=250pF. FP has now dropped considerably to 3654kc/s and FØ180 has just entered at the far end of the scan at 19767kc/s. The magnitude of the impedance has increased as the resonance has strengthened, and the Q of the coil has also increased as lumped element capacitance stabilises the electrical properties of the circuit and dominates over the self-capacitance of the coil.

Fig 2.4. Increasing CP=500pF continues to reduce FP and FØ180. The magnitude of the impedance |Z| continues to fall and the Q reduces slightly.

Fig 2.5. Increasing CP=750pF continues to reduce FP and FØ180. |Z| continues to fall as the parallel resonance weakens, and FP passes through what will be FØ180 of the secondary coil when added to the primary.

Fig 2.6. Increasing CP=1000pF continues to reduce FP and FØ180. |Z| continues to fall, and FP comes into the fundamental band of operation (1810-2000kc/s).

Fig 2.7. Increasing CP=1500pF continues to reduce FP and FØ180. |Z| continues to fall, and FP goes below the fundamental band of operation and into the medium wave (MW) band.

Overall the effect of increasing the primary capacitance CP is to progressively reduce the primary’s fundamental resonant frequency FP. As a better balance between LPCP is established the wide gap between FP and FØ180 reduces. FP appears to go through an optimal point of resonance where the impedance |Z| is maximum and the Q is maximum at a resonant frequency FP ~ 4500kc/s and  CP ~ 195pF. The shifting of FP with CP will allow the complete flat coil 3S-1P to be tuned, as the resonant circuit in the primary interacts with the resonant circuit in the secondary. These two coupled resonant circuits form the overall impedance characteristics of the flat coil as investigated below. No harmonics of the fundamental where observed in the impedance scans of the primary.

VNA-SDR Measurements for 3S-1P

Figures 3. show the wide frequency scan VNA impedance results for Z11 with changing load capacitance on the primary.

To view the large images in a new window whilst reading the explanations click on the figure numbers below:

Fig 3.1. Shows the  secondary and the primary combined together in frequency and with CP = 0pF. Here the two resonant characteristics appear superimposed on one another. The self-resonance of the primary is very clearly defined at M4, and is very similar to that measured in the primary only results of Fig 2.2. The self-resonance of the secondary has generated the fundamental FS = 2254kc/s at M1 and FØ180 = 2437kc/s at M2. For the secondary FØ180 is defined by the effective wire length used in λ/4 mode with the addition of an impedance lowering extension at the bottom-end of the coil. In Part 1 of the design the wire length was to be arranged to give FØ180 = 2400kc/s which is very close to the result measured. The fundamental operating frequency was designed to fall into the 160m amateur band (1810-2000kc/s), and currently FS = 2254kc/s slightly above this band. In operation CP in the primary will be adjusted in order to tune the resonant operating frequency into the required band. The balance between LSCS is much better in the secondary as the self-capacitance of the many turns is much bigger and more stable than that for the primary, and so the gap between FP and FØ180 is smaller, and in this case also contributed to by the series resistance of the secondary coil. Q appears reasonable at this stage and the impedance |Z| is much lower than that for the primary which most likely results from the inter-winding capacitive network of the secondary. There are 2 odd harmonics above the fundamental FS2  at M3 and FS3 at M5 which occur at 3λ/4 and 5λ/4 respectively. It maybe by chance but it is interesting to note that Fis not that far away from 4λ/4 for the secondary. Whether this will have any impact on the performance of the flat coil remains to be established.

Fig 3.2. Increasing CP = 250pF has mainly, and as expected from figures 1, reduced the primary resonant frequency FP down to a frequency much closer to the secondary. Here we can see the start of the formation of the flat coil upper and lower resonant frequencies. The FØ180 point at M2 stays constant as the effective wire length of the secondary is not changing and dominates the fundamental FS of the secondary. The lower frequency FS at M1 from the secondary forms the lower frequency of the flat coil, and starts to move away from FØ180 as CP is increased, which allows tuning of FS to the required frequency using CP. The upper frequency FP at M3 from the primary forms the upper frequency of the flat coil, and moves progressively down towards FØ180 as CP is increased. As two coupled circuits cannot resonate at exactly the same frequency when CP is continued to be increased > 1000pF FS and Fwill appear to swap position, with FP emerging below FS and whilst close to FS appearing to push FS slightly above FØ180. When two or more coupled resonant circuits interact the energy exchange between the modes of vibration creates beating and a particular mode becomes dominant (drives) coupling energy from one resonant circuit to the other. It is in this region that the flat coil is most interesting to investigate, and an important factor in the study of the displacement and transference of electric power. These coupled modes of  FP and FS will be investigated in more detail on Figures 4., and practically within the experiments.

Fig 3.3. Increasing CP=500pF starts to bring the upper and lower frequencies of the flat coil into closer balance. |ZS| at Mis increasing in impedance as the parallel resonance in the secondary is strengthened by coupling from the primary, whilst |ZP| at M3 is reducing. The overall effect is to bring the electric and magnetic fields of induction, across the primary and the secondary, towards a more balanced point. It is this point of balance (harmony between the two induction fields) that is conjectured to be the optimal point to trigger a non-linear event. It is conjectured that a non-linear event at this point of balance, and dependent on the form of the load connected, will generate a coherent displacement event between the generator (source) and the load(s). This consideration will be developed further during the experimental reporting, and in conjunction with actual results obtained.

Fig 3.4. Increasing CP=750pF has now passed through the balance point between the fields of induction and to where the lower frequency starts to dominate the resonance of the flat coil, and the upper frequency will now continue to diminish. The lower frequency FS at M1 is now within the 160m of operation. FØ180 remains unchanged. Harmonics are diminishing as the resonance of the secondary starts to be suppressed by the high capacitive loading of the primary.

Fig 3.5. Increasing CP=1000pF the primary resonance FP is dominating the overall resonance at the lower frequency of the flat coil. Secondary coil harmonics have almost completely been suppressed by the high capacitive loading of CP. The lower resonant frequency at M1 has now moved out of the lower end of the 160m amateur band.

Fig 3.6. Increasing CP=1500pF the primary resonance FP is now totally dominating the overall resonance at the lower frequency of the flat coil. The lower resonant frequency at M1 has now moved into the medium wave band at 1515kc/s.

When CP is lower, and in the range ~200 – 450pF, the overall resonance of the flat coil is dominated by FP the fundamental resonant frequency of the primary, and what has formed the upper resonant frequency of the flat coil ~ 2700kc/s – 4500kc/s. When CP is larger, and >950pF, the overall resonance of the flat coil is again dominated by FP the fundamental resonant frequency of the primary at the lower resonant frequency of the flat coil < 1750kc/s. In between, in the range  450pF < CP < 950pF, there is a more established balance between FS and FP and the upper and lower resonant frequencies of the flat coil are determined by the interaction and energetic exchange between the secondary and the primary. It is this region that is most interesting to experiments in the displacement and transference of electric power, and whose impedance characteristics are investigated in more detail below.

Figures 4. show the narrow frequency scan VNA impedance results for Z11 at a key set of different load capacitance.

To view the large images in a new window whilst reading the explanations click on the figure numbers below:

Fig 4.1. Here the primary capacitance CP = 830pF has been adjusted so that the lower resonant frequency of the flat coil Fat M1 is at the nominal designed point of 1850kc/s in the 160m amateur band. When setup to self-resonate with feedback from the flat coil to the generator the flat coil will stably oscillate at FL, and will form a base starting point for the experiments in the displacement and transference of electric power.

Fig 4.2. Shows the resonant frequency of the primary FP when the secondary is removed from the flat coil, and all other conditions and setup are kept the same. FP is closer to the lower resonant frequency of the flat coil FL than the upper FU, which corresponds with a stronger resonance at FL, and a weaker one at FU, and hence |ZL| > |ZU|.

Fig 4.3. Here the primary capacitance CP = 515pF has been adjusted so that the magnitude of the impedance at the upper resonant frequency is equal to the magnitude of the impedance at the lower resonant frequency |ZU| = |ZL|. It is conjectured that at this point there is balanced interaction between the secondary and primary resonance points which is optimal for the balanced energetic inter-exchange between the electric and magnetic fields of induction between the two coils. It is at this point where best coherence between the two fields of induction can be established, and hence a significant pre-condition to displacement established. It is also conjectured that the initiation of a displacement event requires a non-linear trigger within the system being tested whether that originates from the generator, the coils, or is stimulated as a response (pulled by) the load. It is the purpose of the experimental measurements to establish if this or another mechanism is the case, and the properties and characteristics under which they occur.

Fig 4.4. Again shows the resonant frequency of the primary FP when the secondary is removed from the flat coil, and all other conditions and setup are kept the same. Here we can see that FP at M1 (2577kc/s) occurs almost exactly equi-distant between FS and FP with the secondary added to the flat coil. From Fig. 4.1. (FP – FS) / 2 +  FS = 2548.5kc/s, and from Fig. 4.2. FP = 2577kc/s (<2% difference). Here the resonance of the primary FP has inter-acted with the resonance of the FS so that both contribute equally to the overall flat-coil characteristic and hence establishing the balance between the electric and magnetic fields of induction as discussed in Fig. 4.1.

Fig 4.5. Here the primary capacitance CP = 650pF has been adjusted so that the upper FU and lower FL resonant frequencies of the flat-coil are equi-distant from the 180° phase change frequency of the secondary, FØ180. The resonant frequency of the secondary FS (FL) has just moved into the 160m amateur band at 1956kc/s, and |ZS| wil start to dominate the resonance of the flat coil. When allowed to self-resonate with feedback to the generator the flat coil will stably oscillate at FS.

Fig 4.6. Again shows the resonant frequency of the primary FP when the secondary is removed from the flat coil, and all other conditions and setup are kept the same. FP has progressed down slightly in frequency with increased Cfrom Fig. 4.4. as expected.

Fig 4.7. Calibration test at the end of the measurement period using a standard 50Ω load, with M1 confirming 50Ω at 1850kc/s.

VNA-HP Measurements for 3S-1P

Figures 5. show a selection of frequency results to confirm and check the accuracy of the results from two different VNAs, and also a basic equivalent circuit analysis for the primary S3 the narrow frequency scan VNA impedance results for Z11 at a key set of different load capacitance.

To view the large images in a new window whilst reading the explanations click on the figure numbers below:

Fig 5.1. Shows the 1P primary with CP=0pF as per the measurement of Fig. 2.2. FP at the MKR frequency is 10647kc/s as measured by the VNA-HP, and was previously measured as 9718kc/s as measured by the VNA-SDR which represents ~ 9% variation in this measurements between the two methods. The phase curve indicated by the VNA-HP also shows a large variation corresponding to FP indicating the fundamental resonant frequency of the primary, and some further small impedance variation and phase change at ~18Mc/s. This highlights the difficulty of making measurements directly on the primary where there is a large imbalance between LP and CP which easily leads to varying measurement conditions easily influenced by the surrounding factors such as earthing structures, conductors, and other electrical loading influences. As LP and CP come into better balance this stabalises and a much greater measurement accuracy is obtained between both measurement machines.

Fig 5.2. Increasing CP=750pF as per the measurement in Fig., 2.5. the 1P primary resonant frequency has moved to 2239.25kc/s, and was previously measured as 2233kc/s by the VNA-SDR showing < 0.5% variation in the frequency. |Z| measures as 8.02kΩ, and was previously 9.072kΩ showing ~12% variation. FØ180 measures as 11000kc/s and was previously 11744kc/s ~7% variation.

Fig 5.3. Shows the computed equivalent circuit of the 1P  primary conditions as per Fig. 5.2. The equivalent circuit is calculated by the HP4195A based on a fit model to the measured curve. In part 1 of the impedance measurements the inductance of the 1P primary was measured at 6.453µH, and here is modelled as 6.163µH ~5% variation. The 1P capacitance CP + Cpp =750 + 30.5 = 785.5pF, and here is modelled as 815.91pF ~9% variation. The dc resistance from part 1 was 1.31mΩ and here is modelled as 144.47mΩ. The resonant circuit LPCP shows a reasonably good fit between the measured values and the modelled values. The series resistance of the coil modelled does not correspond to that measured, although it is considered that this difference does not significantly effect the quality factor of the flat coil, or assessment of the small signal impedance measurements thus far.

Fig 5.4. Shows the secondary added to form the flat coil 3S-1P where CP=0pF. As per Fig. 3.1 for the secondary and primary impedance-frequency responses become superimposed on one another. The primary resonance FP can be identified clearly at 11000kc/s along with the gradual phase chanhge, along with the secondary resonance FS at 2189.5kc/s with a variation of ~3% from the VNA-SDR measurement of 2254kc/s. Secondary harmonics can be identified in a similar way in a corresponding frequencies as per Fig. 3.1. The greater sensitivity and more finally tuned input circuits of the VNA-HP also show a strong additional resonance at FS4 at ~17.5Mc/s which is not identified in Fig. 3.1.

Fig 5.5. Shows primary capacitance CP= 830pF as per Fig. 4.1 where the lower resonant frequency of the flat coil FL has been adjusted to be at the designed frequency of 1850kc/s. The VNA-HP shows a close correlation at 1851.75kc/s ~1% variation, and corresponsing close correlation of FØ180 and FU.

Fig 5.6. Shows primary capacitance CP= 515pF as per Fig. 4.3. Here the FØ180 point is compared at 2390.75kc/s and 2418kc/s a variation of ~3%.

Fig 5.7. Shows primary capacitance CP= 650pF as per Fig. 4.5. Here the FU point is compared at 2819.5kc/s and 2875kc/s a variation of ~2%.

It has been shown that there is good correspondence of the key impedance features of flat coil 3S-1P when measured on both VNA-SDR and VNA-HP. The variation between measured parameters is acceptable for the intended purpose of the flat coil, and all the various measurements correlate well in drawing key conclusions regarding the impedance-frequency properties in part 2.

Summary of the VNA results and conclusions so far:

1. The fundamental resonant frequency impedance characteristics of the primary FP, have been shown to interact with that of the secondary FS to produce an upper and lower resonant frequency for the flat coil, FU and FL.

2. FU and FL can be adjusted in frequency by adjusting CP, which also leads to changes in |ZU| and |ZL|. Adjustment of CP allows the frequency band of operation to be selected, and occurs for FL within the target operation band, the 160m amateur band.

3. The balance of |ZU| and |ZL| leads to several important operating points for the experiments in displacement and transference of electric power. Most particularly when |ZU| = |ZL| and it is conjectured that the magnetic and electric fields of induction are in balance between the primary and secondary, which will lead to the best operating point for coherence between the induction fields and hence displacement events stimulated by non-linear events in the system.

4. The correspondence between measurements using different VNAs is good with variations in most key parameters being < 5%.

5. Equivalent circuit elements yield circuit values in reasonable correlation to those expected and those measured in part 1.

6. Small signal input impedance measurements Z11 have provided greater understanding and insight into the mechanisms governing the characteristics of the flat coil, how best to experiment using the flat coil, and how best to drive and match the coil to the various generators and loads.

Click here to continue to the flat coil impedance measurements part 3.

 

Flat Coil Impedance – Part 1

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

With the secondary 3S removed:

Inductance L: 6.453µH @100kc/s

Impedance Z: 4.055Ω @100kc/s

Resistance R: 0.00131Ω @100c/s

DC Resistance R: 0.00Ω

With the secondary 3S added:

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

With the secondary 3S removed:

Inductance L: 290.98µH @100kc/s

Impedance Z: 182.82Ω @100kc/s

Resistance R: 0.5758Ω @100c/s

DC Resistance R: 0.70Ω

With the secondary 3S added:

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

With the secondary 3S removed:

Frequency of dip meter maximum: 2625kc/s

With the secondary 3S added:

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.

 

Flat Coil Construction

The flat coil design has provided the necessary dimensions and materials for the secondary and primary coil to be constructed. This post will outline construction of the 3S-1P flat coil described in Part 3 of the design. The complete constructed flat coil is shown in Figures 1. below, and gives an overall impression of how the coil has been mechanically designed to accommodate the required electrical coil design for a range of different experimental scenarios.

The overall required specification from the design process is summarised as follows, and can then be considered for the mechanical design and construction:

Secondary specification (3S):

Geometry: 2 spiral coils interleaved per turn

Number of turns: 20

Coil Inner diameter: 345mm

Coil Outer diameter: 455mm

Wire length: 25.132m

Wire type: RG178 braided coax with the outer braid connected only

Calculated inductance (assuming solid wire): 142.8µH

Primary specification (1P):

Geometry: spiral turns in same plane and outside the secondary

Number of turns: 2

Coil inner diameter: 525mm

Coil outer diameter: 575mm

Calculated wire length: 3.455m

Wire type: AWG10 1050 / 40 Silicone coated micro-stranded wire

Calculated wire length to equal primary and secondary conductor weight: 3.50m (2% error from calculated wire length to allow for 2 complete turns and connection)

Calculated inductance (assuming solid wire): 4.8µH

Frequency specification:

Secondary resonant frequency 180° phase change: 2400kc/s

Secondary tuned fundamental resonant frequency: 1810 – 2000kc/s

Calculated parallel primary tuning capacitance to match the secondary 180° phase change frequency: 916pF (assuming 4.8µH primary inductance)

Ideal parallel primary tuning capacitance: 100pF – 1200pF 4kV vacuum capacitor

Fig. 2. below shows the plan for the flat coil mechanical design with the key supports, secondary, and primary coil positions and dimensions indicated.

The back board uses 12mm thick finished interior plywood, and has four quarter circle cut-outs to remove the excess material from around the secondary coil. The back board is supported on a plywood or nylon base with a support pillar in the back to prevent warping of the plywood back board over time.  It is useful to varnish the back board if the coil is to be used outside, to afford some protection against moisture absorption into the wood.

The coils are supported on the back board by 16 PTFE or Neutral Nylon 66 supports and have the dimensions 190mm x 50mm x 12mm (LxHxW). These supports have 2.5mm wide grooves cut 9.0mm deep from the top edge to retain the windings of the secondary coil. Three grooves where also cut outside of the secondary ID and OD to allow for rewinding adjustments during experimentation. In total 17 grooves (11 for the secondary and 3 either side) were cut to accommodate the windings of the secondary coil. The windings of the secondary coil are retained in the slots by sprung nylon straps screwed to the coil supports using tapped M3 nylon screws. This method of retaining the secondary was used rather than a more permanent gluing approach, to allow the windings to be adjusted, rewound, or even changed in specification or wire type if required. The coil supports were mounted to the back board using M6 countersunk nylon screws. No metal screws or attachments were used in close proximity to the coils.

The outer top ends of the coil supports have an additional 3 x 6.0mm grooves cut 8mm deep to accommodate the windings of the primary wire. In addition each of the primary grooves was cut with a thin narrow slot (1mm wide) and 20mm deep to accommodate the flat copper strip primary (3P) if required. The bottom most coil support has a nylon mount for a high voltage output terminal connected to the outer end of the secondary coil. The inner end of the secondary conductor can be fed to a range of different mounts including a BNC connector for a telescopic aerial, a ceramic bulb-holder mounted on a nylon support for a neon bulb, or other high voltage terminal, feed, or top-load. The primary coil ends are fed through the back board, (via insulated conduits if necessary), and then attached directly to the primary capacitor at the primary length established in the equal weight of copper calculations in the part 3 of the design.

The early versions of the flat coil used solid nylon coil supports fixing the secondary and primary onto the back board. A later version of the flat coil, (as shown in the Figures 1. and 3.), used two-part coil supports arranged in such a way that the complete secondary unit can be removed from the primary and back board. This mechanical design greatly assists measurements of the secondary and primary independently whilst still in-situ to the experiment or circuit being measured. In the frequency measurements it is desirable to remove the secondary coil from the system and test the primary properties before adding the secondary, which then provides a much clearer understanding of how the two coils interact in the electrical system.

The secondary windings and the primary windings are normally wound in the same rotation direction on a single flat coil. A clockwise wound secondary will have a corresponding clockwise wound primary. For experiments involving displacement and transference of electric power between two flat coils the coil winding direction would ordinarily be in counter-rotation between the two flat coils, so as to define a clear boundary for the electric and magnetic fields of induction between the two coils. For example, if the flat coil attached to the generator has its windings wound clockwise, then the flat coil attached to the load will have its windings wound anti-clockwise. The flat coil winding possibilities have been measured, and the differences noted, for first, two flat coils counter wound, then secondly two flat coils wound in the same direction, and thirdly even with a single flat coil with counter-wound secondary and primary coils. These differences and their effects on the boundary conditions for the electric and magnetic fields of induction will be reported and considered in the measurement and experimental posts.

The secondary winding was wound onto the coil supports to create two inter-leaved coils as suggested and demonstrated by Dollard[1]. The lower turn is wound into the bottom of the coil support groove starting from the required secondary OD position. After the first complete turn nylon supports, fashioned from trimmed nylon M3 screws, were inserted into the groove to provide the correct spacing between the upper and lower coils. The depth of the groove and the spacer were so arranged so that the spacing between the two coils was ~60-65% of the conductor winding pitch. It has been suggested by Dollard[2] that this winding space is optimal for the inter-winding capacitive network and hence advantageous in generating the Longitudinal Magneto Dielectric (LMD) wave or standing wave.  The formation of the LMD wave is conjectured as a necessary pre-condition for the generation of a displacement event when combined with a non-linear element, load, or event in the system.

To investigate and confirm the 60-65% spacing, a flat coil has also been assembled where the upper and lower coils are wound directly on top of each other with no nylon spacer, and only spaced by twice the thickness of the insulating jacket around the conductor of the winding. In the case of the 3S coax braid coil the conductors are spaced by 0.5mm without the nylon spacer, and by 3.0mm with the spacer. In the case of the 1S PTFE coated stranded wire the conductors are spaced by 1.0mm without the nylon spacer, and by 3.5mm with the spacer.

With the spacer in place above the lower winding the upper turn is now added to the coil. When one complete turn has been wound the wire in the upper coil will move to the lower coil in the next adjacent groove of the coil support. This continues until 10 complete grooves have been wound, which corresponds to an inter-leaved upper and lower flat coil of 10 turns each, and 20 turns in total. After the 10 complete grooves have been wound the coil length can be fine adjusted by a fraction of a turn (e.g. 0.5) before being terminated at the conductor centre mount.

In later versions of the flat coil the back-board was modified to provide mounts for using the coil vertically, horizontally, or with nylon threaded mounts to attach legs so that the coil can be used horizontally outside or on the bench. This combination of fixtures allow for a wide range of experimental conditions including outside as well as inside in the lab or workshop.

Detailed pictures of the mechanical construction are shown in Figures 3. below.

Click here to continue to the flat coil frequency measurements part 1.


1. Dollard, E. & Lindemann, P. & Brown, T., Tesla’s Longitudinal Electricity, Borderland Sciences Video, 1987.

2. Dollard, E., Theory of Wireless Power, Borderland Sciences Publication, 1986.

 

Flat Coil Design – Part 3

Following on from part 2 it has been establised that the primary and secondary coils will be so arranged to contain equal weights of conductor, dependent on the geometry of the specific conductors being used, and so to ensure the continuity of conductor boundary conditions and hence the balance, continuity and coherence of the electric and magnetic fields of induction between the primary and the secondary coils.

It is important in the primary to maximise the current carrying capability of the coil, which will allow the generator or tank circuit to provide strong oscillations, bursts, and impulses, according to the type of experiment to be undertaken. This means that the inductive reactance of the primary should be as low as possible within the band of frequencies required, allowing a large current to flow, and whilst also allowing for a practical value of tank capacitor with sufficient adjustment to tune above and below the frequencies of interest. In this case it is intended to use a variable high voltage vacuum capacitor in the range 100pF – 1500pF, with the desired fundamental resonant frequency change at 2400kc/s occurring at a tank capacitance in the range 900pF – 1100pF which allows for good adjustment for the variable vacuum capacitor, but also for the ease of use of a fixed high voltage capacitance of 1000pF (1nF). For the tank capacitance to be 1000pF, and in the ideal theoretical case, the  inductance of the primary would be 4.4uH.

Accordingly, and in consideration of the 20 turns in the secondary designed in part 1, the number of turns in the primary will be fixed at nominally 2, and with the ability to tap the primary, (for use with bare metal primary materials only e.g. copper tube or strip), slightly above or below the exact 2 turns mark should a finer resolution of tuning be required. This gives a voltage magnification in the magnifying transformer according to the secondary-primary turns ratio of 10, which is high enough to magnify the generator voltages to a more usable level in the observation and measurement of displacement events, and yet still low enough to allow high voltage generators to be used in the tank circuit without causing excessive breakout and discharge, and hence dissipation of energy to the surrounding environment, from the secondary.

Wire spacing between the turns of the primary is to be arranged to avoid any possibility of electric discharge through sparking when the primary is driven at resonance from a high voltage generator such as a vacuum tube oscillator or linear amplifier, a static or rotary spark gap generator, or other high voltage generator such as a vintage diathermy machine or electro-therapy generator. This means that the wire spacing in the primary should be safe for potentials up to 20kV applied across the primary terminals by a generator, and contacts to the primary and the primary conductor size should be able to support total input powers up to 2.5kW. With this considered the nominal distance between the start of the outer turn and the end of the second inner turn was set at 25mm, which gives a turn spacing of 12.5mm. The generally accepted dielectric strength of air at normal temperature, pressure, and humidity is 30kV/cm. When using a bare copper 3/16″ or 4.8mm tube this leaves the gap between conductors in the primary of 7.7mm which would have a nominal breakdown voltage in air of ~ 23kV, which is considered adequate for the highest voltage generators currently used in this research. The centre diameter of the primary coil was determined empirically by adjustment in relation to the secondary where the Q of the final coil was maximised, and a coupling factor between the primary and most outer turns of the secondary of ~ 0.15 was achieved.

With these characteristics defined the primary wire length could be defined to best match the required characteristics. Again the spiral coil calculator was used to assist in this calculation:

From Fig. 1. the required primary coil wire length is 3.455m, which theoretically yields a coil inductance of 4.8uH. At 2400kc/s for the desired fundamental resonant frequency phase change this yields a tank capacitance of 914pF, which is within the range required in the flat coil design.

Conductors to be used / tested in the secondary coil include:

1S. PTFE / Teflon coated, silver plated, multi-stranded wire. The strong PTFE coating prevents spark or streamer breakouts from running along the length of the wire, and the silver coating bonds the jacket firmly to the inner wire conductor. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: Awg16, 19/0.3 (19/29), ID ~ 1.35mm, OD ~ 2.5mm, white PTFE jacket.

2S. Silicone coated, flexible high density micro-stranded wire. The high number of conductor strands make this wire suitable for a higher frequency, lower-loss winding, and the silicone coating makes the wire very flexible with good high voltage and temperature properties. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: Awg16, 252 strands, ID ~ 1.5mm, OD ~ 3.0mm, black silicone jacket.

3S. Braided shield coaxial cable. The outer shield to be used as the conductor with many strands maximising the inter-turn capacitance, and the conductor surface area, and with the inner coaxial conductor non-connected. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: RG178 Coaxial cable OD ~ 2.50mm, transparent Teflon jacket.

Conductors to be used / tested in the primary coil include:

1P. Silicone coated, flexible high density micro-stranded wire. The high number of conductor strands make this wire suitable for a higher frequency, lower-loss winding, and the silicone coating makes the wire very flexible with good high voltage and temperature properties.

2P. Flexible copper tubing, with good high current capability and easy primary tapping to the bare conductor surface.

3P. Copper strip, with high surface area, high current capability, and highest Q for the high frequency experiments.

The early versions of the flat coil used wire combination 1S-1P for both the generator and load coil, providing an easy to use coil structure suitable for a wide range of preliminary investigations into the displacement and transference of electric power. This was later replaced by 1S-3P as the best measured for both the generator and load coil for experiments with displacement events. Later experiments in telluric transmission of electric power used the 1S-3P combination as the best measured generator coil, and with 3S-1P as the best measured load coil. The details of these measurements and there results will be reported in the experimental posts.

For calculations of copper weight, volume, and other useful data with respect to solid and stranded wires, and where either exact specification data, or measured data, is not available for the actual wire used, the following wire and cable data from Calmot can be used.

Click here to view or download the Calmot wire and cable data.

1. For coil 1S-1P the equal weight of copper calculation:

Secondary wire length (from part 2): 25.132 m

Specification unit weight of actual wire used: 11.120 kg/km

Secondary wire weight = 11.120 x 25.132 / 1000 = 0.279 kg

Calmot data for 8 AWG 1666 / 40: 81.1 kg/km

Actual primary wire 1P 8 AWG 1600 / 40 = 1600 / 1666 x 81.1 = 77.887 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.279 x 1000 / 77.887 = 3.582 m

Calculated primary wire length from flat spiral coil calculator in Fig. 1: 3.455 m

1P Primary wire length of silicone coated micro-stranded 8 AWG 1600 / 40 = 3.58 m

2. For coil 1S-2P the equal volume of copper calculation:

Secondary wire weight (as above) = 0.279 kg

Measured unit weight of pure copper pipe OD 4.75mm (3/16″), wall thickness 0.8mm: 77.420 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.279 x 1000 / 77.420 = 3.603 m

2P Primary length of 4.75mm (3/16″) pure copper pipe = 3.60  m

3. For coil 1S-3P the equal weight of copper calculation:

Secondary wire weight (as above) = 0.279 kg

Specification unit weight of pure copper strip 30mm wide and 0.3mm thick (standard strip available): 80.450 kg/km

Required primary strip length for exact equal secondary and primary weights = 0.279 x 1000 / 80.450 = 3.467 m

3P Primary length of 30mm x 0.3mm pure copper strip = 3.47  m

4. For coil 3S-1P the equal volume of copper calculation:

Measured unit weight of RG178 outer braid only: 6.150 kg/km

Secondary wire weight = 6.150 x 25.132 / 1000 = 0.155 kg

Actual primary wire 1P 10 AWG 1050 / 40 = 45.150 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.155 x 1000 / 45.150 = 3.433 m

1P Primary wire length of silicone coated micro-stranded 10 AWG 1050 / 40 = 3.50 m (2% error to allow for 2 complete turns and connection)

All required primary lengths, (other than case 4 where the primary must be extended for 2 complete turns), are longer than the flat spiral coil calculation of 3.455m, which allows for 2 full turns of the primary and connections to be made to the primary capacitor. Connections to the primary capacitor are arranged at the point where the primary length is equal to that required to equal the weights of the secondary and primary coils.

It must also be noted that the primary capacitor introduces a weight of conductor into the primary circuit calculation which has not been accounted for above. In the experimental stage different capacitor sizes and weights will be used to determine the overall induction field mismatch caused by this circuit element and/or other elements in the generator or load. In the case of diminished displacement and transference of electric power results, the primary weight of copper will need to be adjusted through reduced AWG size (P1), reduced tube diameter (P2), and reduced strip width (P3), in order to get the best equal conductor weight match.

This concludes the three design parts for the flat coil with all the necessary parameters for construction of the final coil.

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