Design and implementation of a Tesla coilChristopher Rutherford20 April 2012

Introduction

Scope and context

Tesla coil theory and operation

Tesla coil design Lumped circuit equations JavaTC calculator

Measurements

Conclusions

Scope and Context

Objectives Learn about Tesla coils Make system that works Satisfy an interest

Constraints Use easily available parts and equipment Keep costs to a minimum Carried out in spare time

Remarks Wheeler’s and Medhurst’s formulas are empirical

TC Operation

Resonant transformer Lumped vs distributed Spectrum analysis Spherical artefacts

Secondary envelope and coupling

Tesla coil Implementation

Tesla coil parameters

Rotary spark gap Asynchronous

2 breaks per rotation 50Hz (3000 RPM) Average power proportional to break rate Synchronous

Counter rotating 2 * 8 contacts per disk Breaks per second is 16 * rotational speed <1000 bps

NST Protection filter Remove any RF that could damage NST Series MOV, series resistors, series capacitor

Tesla coil parameters

Multiple miniature capacitors(MMC) (20s, 3p) 220nF @ 1.5KV = 33nF @ 30KV

NST Power Supply 4 * (25mA * 10KV) = 1KVA

Coils (Wheelers formula, inches) Primary, Spiral coil, 10cm to 24 cm

L = ( N*R )^2 / ( 8*R + 11*W ) =14uH

Secondary, helical coil, 5cm * 72cm L = ( N*R )^2 / ( 9*R + 10*H ) =26mH

Tesla coil parameters

Secondary capacitance Self, Medhurst equation (cm) , est 1940s

C/d = 0.1126(l/d) + 0.08 + 0.27√(d/l ) pF/cm (0.81 + 0.08 + 0.1)*10 = 9.9 pF Top load C = (25.4*R) / 9=12 pF

Total 24pF Resonant frequencies

F = 1/( 2 * PI * ((L * C)^0.5) Primary 14uH and 0.033uF gives 234Khz Secondary 26mH and 22pF gives 210Khz

V secondary Vs= Vp(Cp / Cs)^0.5=387Kv

JavaTC coil design for comparison

JavaTC

Ls=23.7mHCs=16pF

Lp=12.9mHCp=0.033uF

Fp=243KhzFs=256Khz Accounts for variations in inductance's and

capacitance's due to the non-uniform current distribution  at F0

Measurements

Experiments carried out 6 years ago, Equipment in storage

Email“Measured F0 by connecting oscilloscope and signal

generator to base of TC, fo=250KHz. These figures in JAVATC produce fo= 252.9KHz so I'm happy with the 1% error.”

Can also see on F0 photo of secondary envelope, which appears to show same resonant frequency

Measurements

Email“Pri, C=10nF, RSG short circuited, one side of pulse cap

to ground and sig gen and osc on other side I see a resonant frequency at 285KHz. 9 turns, pancake, start radius=10 cm and radius=26 cm cable dia= 0.5cm. These figures in JAVATC produce fo= 282.31KHz so I'm happy with the 1% error.”

Primary capacitor later upgraded to 33nF Used “Have JAVATC tune Primary Coil” to

compensate for new capacitor. Striped away insulation at 5.8 turns (can see on photo)

Measurements

Measurements

Measurements

Assume 20us / div (could be wrong)

F0=1/(20us/5)=250KHz

Total energy transfer time 20us/0.55=36uS (javatc 22.98)

Half cycle energy transfer 5*2 half cycles / 0.55 cycles =10 ( javatc 11.24)

Measurements

Output power proportional to ark length

P=(L/1.7)^2 = (35/1.7)^2=423W

~50% losses Primary spark Resistance Radiation

Conclusions

Observation Tesla coils follow known principles

(To a certain extent)

Performance Improvements Higher/Tight coupling (k=0.6) Lower height to width ratio Lower losses in secondary

Conclusions

Future investigation More analysis at low power Solid state Tertiary coils Higher break rate (power proportional to break rate)

Questions / Answers