The Practical Guide To Ultrasonic Testing In The Real World Andrew Cunningham
www.practical-ndt.com
[email protected]
The Practical Guide to Ultrasonic Testing In the Real World
The Practical Guide to Ultrasonic Testing In the t he Real World © Andrew Cunningham 2008 All rights reserved. Published by Practical NDT. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, printed, photocopying, recording, or otherwise, without the prior written permission of the author. Nothing contained in this book is to be construed as a grant of any manufacture, sales or in connection with any method, process, apparatus, product or composition, whether or not covered by letter patent or registered trademark. Printed in Canada by PageMaster Disclaimer
The author assumes no responsibility for the safety of persons using the information in this book. This book is for information only.
ISBN 987-0-9809893-0-4 987-0-9809893-0-4 Second printing
2
Table of Contents Preface ............................. Preface............... ............................. .............................. .............................. ............................. ............................. .............................. ............................... ....................... ....... 5 Sound............. Sound. ........................... .............................. ............................... ............................... ............................. ............................. .............................. .............................. ......................... .......... 6 Compression Waves ............................... .............................................. .............................. ............................. ............................. .............................. ............................. ................ 6 Shear Waves...................................... Waves................................................... ............................ ............................... ............................. .............................. ............................... .................... ...... 8 Lobes, Cones, and Other Myths.......................... Myths........................................ ............................. .............................. ............................. ............................... ..................... 9 Compression and Shear Waves Travel Together.............. Together ........................... ............................ .............................. ............................ .................. ..... 11
λ
Quick Calculations of the Wavelength ( ) ............................. ............................................ ............................... ............................. ......................... ............ 14 Amplitude and Decibels........................ Decibels....................................... ............................. ............................. ............................ ............................ ............................. .................. .... 15 The Screen Display ............................ ........................................... ............................... ............................... .............................. ............................. ............................... ................. 16 The Ultrasonic Flaw Detector ............................ ............................................ ............................... .............................. ............................. ............................... ................. 18 The Straight Beam Probe and the Dead Zone ............................... .............................................. .............................. ............................. .................. .... 22 Near Zone / Far Zone (Fresnel Zone or Near Field / Far Field).......................... Field)....................................... ............................ ............... 27 Measuring the Initial Pulse (I.P.)............................... (I.P.)............................................. ............................. .............................. ............................. .......................... ............ 31 Reflection, Scatter and Acoustic Shadow...................................... Shadow..................................................... ............................. ............................. .................... ..... 32 Thickness Measurements.......................... Measurements......................................... ............................. ............................. ............................... ............................... ......................... .......... 33 Checking the Probe Prior to Measuring.................................... Measuring................................................... ............................ ........................... .......................... ............ 34 Measuring a 0° Probe ............................. .............. ............................. ............................. .............................. ............................. ............................. ...................... ....... 35 Calibrating with for Different Alloys.............. Alloys ............................. ............................. ............................. .............................. ............................. ............................... ................. 36 Know Your Probes ............................ .......................................... ............................. .............................. ............................. ............................. .............................. .................... ..... 37 Using the IIW V1 Block................................... Block................................................. ............................. .............................. ............................. ............................... ...................... ..... 40 Calibrating to Shear Wave............................ Wave............................................ ............................... .............................. ............................. ............................... ...................... ..... 41 Scanning with a 0° Probe.......................... Probe......................................... ............................. ............................. .............................. ............................. .......................... ............ 43 Sizing Holes in Machined Parts.............. Parts ............................ ............................. .............................. ............................. ............................. .............................. ............... 44 Grid Scan ............................. ........................................... ............................... ............................... ............................. .............................. ............................... ............................... ............... 46 Scanning for Internal Pits ............................. ............................................ .............................. ............................. ............................. .............................. ....................... ........ 48 Scanning for Pits on a Curved Surface (Vessels and Piping) ............................. .......................................... ............................ ............... 50 Scanning for Volumetric Integrity............................... Integrity.............................................. .............................. ............................. ............................. ......................... .......... 51 Shear Wave Scan ............................. ........................................... ............................. .............................. ............................. ............................. ............................... .................... .... 52 Mode Change, Creeping Wave or Internal Acoustics???............ Acoustics??? ........................... ............................ ............................ ....................... ........ 53 Distance-Amplitude Correction Curve ........................... .............. ............................ ............................. ........................... ......................... ............ 56 55 How to Construct a DAC Curve (DAC) ............................ .............. ............................. .............................. ............................. ........................... .............................. ................. How to use the DAC Curve ............................. ............................................ .............................. .............................. ............................. ............................. .................... ..... 56 Making the Transfer Loss DAC ........................... ......................................... ............................... ............................... ............................. .............................. ............... 57 Setting Sensitivity............... Sensitivity .............................. ............................. ............................. ............................... ............................... .............................. ............................. .................. .... 58 Plotting System ............................. ............................................ ............................... ............................... .............................. ............................. ............................... ...................... ..... 59 Locating the Reflector Depth with Simple Mathematics......................... Mathematics........................................ ............................. .......................... ............ 60 Finding the Position in Front of the Probe ........................... .......................................... ............................. ............................. .............................. ............... 60 Finding Depth as a Percentage ........................... ......................................... ............................. .............................. ............................. ............................... ................. 62 Sizing Techniques ............................. ........................................... ............................. .............................. ............................. ............................... ............................... .................. .... 67 Sizing for Length with Max Amp ........................... ............................................ ............................... ............................. .............................. ............................ ............. 68 Sizing for Length with 6dB Drop ............................. ............................................ ............................. ............................. .............................. ............................ ............. 70 Sizing for Length with 20dB Drop ........................... .......................................... ............................. ............................. .............................. ............................ ............. 72 Total Drop............................. Drop........................................... ............................... ............................... ............................. .............................. ............................. ............................... ................. 73
©2008 Andrew Cunningham
3
The Practical Guide to Ultrasonic Testing In the Real World
Combination of all Sizing Techniques........................ Techniques....................................... .............................. ............................... ............................... ....................... ........ 74 Cross Sectional Sizing Techniques ............................. ............................................ ............................. ............................. .............................. ....................... ........ 76 Finding the t he True Angle ........................... ......................................... ............................. ............................... ............................. .............................. .............................. ............. 78 Cross Sectional Sizing with Maximum Amplitude Technique ........................... ........................................ ............................ ................... 79 Interpretation by Cross Sectional Drawing ............................. .............................................. ............................... ............................. ......................... .......... 82 Cross Sectional Sizing with 6dB Drop ............................ ........................................... .............................. ............................. ........................... .................... ....... 85 Cross Sectional Sizing with 20dB Drop ............................ .......................................... ............................. .............................. ............................. .................. .... 88 Probe Manipulation ............................ ........................................... .............................. ............................. ............................. .............................. ............................. .................. .... 91 Echo Interpretation............. Interpretation ............................. ............................. .............................. ............................... ........................... .............................. ............................... .................. .... 92 Cracks ........................... .......................................... .............................. ............................. ............................. .............................. ............................. ............................... ......................... ........ 93 Lack of Side Wall Fusion.............. Fusion ............................. ............................. ............................. .............................. ............................. ............................... ......................... ........ 94 Lack of Root Ro ot Fusion ............................. ............................................. ............................... .............................. ............................. ............................. .............................. ............... 95 Lack of IInterpass nterpass Fusion .............................. ............................................. .............................. ............................. ............................. .............................. ....................... ........ 96 Slag Inclusion............... Inclusion ............................. ............................. .............................. ............................. ............................. .............................. ............................... .......................... .......... 97 Isolated Gas Pore.................. Pore................................... ............................... ............................. .............................. ............................... ............................... ............................ ............. 99 Porosity Cluster ............................. ............................................ .............................. ............................... ............................... ............................. ............................. .................... ..... 100 Concave Root ("Suck (" Suck Up") ............................. ........................................... ........................... ............................ .............................. .............................. ..................... ...... 101 Bad Pick-Up ("Stop-Start") ............................. ........................................... ............................. .............................. ............................. ............................... .................... ... 102 Misalignment (High/Low) and, or Mismatch........................... Mismatch......................................... ............................. ............................ .......................... ............. 103 Tricks of ............................ the Trade ............................. ............... ............................. ............................... ............................... .............................. ............................. ............................. ............... 104 Flanges .............. ............................... ............................... ............................. ............................... ............................... .............................. ............................. ................ .. 104 T K Y Joints.............. Joints ............................. .............................. ............................. ............................... ............................... ............................. .............................. .......................... ........... 105 End Scans of Welds ............................. ............................................ ............................. ............................. .............................. ............................. ............................. ............... 105 Nozzle to Shell Welds and Node Plates ........................... ......................................... ............................. .............................. ............................. .................. 106 Sizing "invisible" Flaws.............. Flaws ............................ ............................. ............................... ............................... .............................. ............................... ........................ ........ 109 Nozzle Testing........................... Testing......................................... ............................... ............................... ............................. .............................. ............................. ........................ .......... 112
4
Preface During my career, which spans over 30 years, in non-destructive testing and ultrasonics, I have developed many tricks and alternative techniques that, I believe, improve accuracy and results while keeping the job simple and efficient. At the same time, I have also paid attention to whether the data I was seeing corresponded with everything I was taught during my level II training in the UK. I was surprised to find the the ultrasonic effects th that at I saw every day were often nev never er mentioned, and were even contradicted by the accepted texts and tutorials. In this book I have put together some ‘tricks of the trade’, inspection techniques, and beam plot that I thought useful. Parts of this book may sound controversial, but these techniques have been the mainstay of my daily work and have been backed up by many years of experience and experiment. My intent is for this book to be used by the qualified technician so as to improve his skills, the quality of his results and his efficiency in the daily challenges to be met by the NDT industry. Due to some of its controversial content I must caution that it is not recommended for exam preparation. I have endeavoured to make this manual clear, concise and user-friendly. I hope you find this book useful and that it allows you to challenge the more traditional and orthodox techniques we were all taught to enable us to qualify. Please let me know if you disagree or would like to que question stion anything I have written. Your feedback is most welcome.
Andrew Cunningham
[email protected] [email protected]
©2008 Andrew Cunningham
5
The Practical Guide to Ultrasonic Testing In the Real World
Sound The purpose of this section is to give you simple and effective ways to understand and visualise how ultrasonic waves travel. Sound is the movement of vibrating atoms and molecules!!!! Infrasound is the movement of the vibrating atoms below the normal human hearing range of about 20 cycles per second (which can also be stated as 20 Hz). Infrasound vibrations may be felt by the hand, depending on the intensity. Audible sound is the movement of atoms that vibrate at cycles between 20 Hz and 20 kHz. These are the accepted average figures and are not absolute (a child’s hearing range is generally higher, while the range of older members of society is typically lower). Ultrasound is the movement of atoms that vibrate at a rate greater than 20 kHz and above the accepted norm of the human hearing range.
Compression Waves Propagation of Sound
Sound propagates through solids, liquids and gases as one atom knocks against the next in a chain reaction. The first motion we will discuss discuss is the compression wave. An example is Newton's cradle (Fig. 1) where energy is passed along the line of balls at such a high velocity that the swinging out of the end ball appears to be instantaneous. The speed (or velocity) with which the energy passes through these balls is approximately 6 kilometres per second, and can be considered an analogy to the compressive wave form of sound through solid metals.
Fig. 1
6
The compression wave is the most efficient way of transmitting sound mechanically through any medium — gases, liquids or solids. Moving in the line of the wave motion, each atom travels only a small distance before striking the next atom(s) and passing the energy on. This enables the waveform to travel at high speeds with minimal loss of energy. In their natural state, the atoms can be considered stationary and equally spaced (Fig. 2).
Fig. 2 In ultrasonics the crystal strikes the atoms, and displaces them (Fig. 3). The atoms will take the path least resistance out ofatthe way6as quick as ppossible and(KPS) will compress into kilometres their of neighbours, passingasonthey themove vibrations about er second in steel. This compression wave will radiate out from its point source in all directions, creating a wave hemispherical in shape when viewed from the surface.
Fig. 3
©2008 Andrew Cunningham
7
The Practical Guide to Ultrasonic Testing In the Real World
Shear Waves
Fig. 4 The elastic properties of the material will allow the atoms to vibrate, setting up a secondary wave form, known as shear wave, due to the shearing motion in relation to the direction of propagation (Fig. 4). In a solid, it is impossible to create a compression wave without a secondary shear wave form being generated, and it is likewise impossible to generate a shear wave without creating a compression wave first.waveforms Because the atoms are in allwith 3 dimensions in a wave solid, front. both the compression and shear will radiate in alllinked directions a hemispherical
Fig. 5 (red) and one shear (blue) (blue) — Figure 5 shows two spherical wave forms — one compression (red) radiating out from the point of impact (the front top left hand corner).
8
Lobes, Cones, and Other Myths Ultrasonic textbooks usually have diagrams such as the one below (Fig. 6) that show the UT beam firing straight out of the probe in a "flame" configuration. This type of diagram can be misleading and dangerous to the technician. First of all, sound radiates from its source as a hemisphere regardless of frequency. The "flame like" model makes it look like all the sound propagates in one direction. One wave motion cannot be generated without generating another. Sonic Lobes Transducer
Bea eam m S re read ad Fig. 6 Psychedelic pictures from the 70”s and 80”s showed interference patterns generated in a liquid or jelly that were very misleading. There T here are no such things as lobes. Beam spread is a complete misnomer; there is no conical effect of sound motion. The angle and the receptive angle range of probes are down to the design and efficiency of the transducer and cannot be calculated by the beam spread formula. The above, though obvious, contradicts what technicians are taught.
Experiment to demonstrate the hemispherical principle
To show that sound will radiate (propagate) hemi-spherically regardless of frequency, a simple demonstration can be done with two 0° probes. 1)
The flaw detector is to be calibrated with a single 0° probe, with a test range of 100mm across full screen.
2)
Connect the second 0° probe to the flaw detector, and set the control to “dual” or “through transmission”.
3)
Place the transmitter probe (shown in blue) blue) onto the IIW V1 (Fig. 7) at the side of the 100mm radius notch. red)) on the opposite side, directly underneath the Place the receiver probe (shown in red
4)
transmitter. ©2008 Andrew Cunningham
9
The Practical Guide to Ultrasonic Testing In the Real World
5) 6)
7)
The first signal on the screen will be a compression wave that will appear at 50mm on the time base. Move the receiver probe to the 91mm land and the signal will appear from 45.5mm, increasing as the probe is slid along the 40mm long land to the corner of the land to the 100mm radius until the signal is at 50mm on the screen. Add 20 dB to compensate for the loss of probe contact area. Place the receiver probe on the 100mm radius bottom corner. The signal will be at 50mm on the screen. As the receiver is moved around the 100mm radius, the signal will remain at 50mm with minimal drop in amplitude, until 85°, contrary to the "flame like" model.
Fig. 7 IIW V1 Calibration Block As the receiver probe is slid from the bottom corner around the 100mm radius, a second low amplitude signal will break off of the first 50mm signal. This is the echo of the first back wall echo compression wave, which travels across the screen, increasing in distance as the receiver probe moves towards the top of the 100mm radius. To confirm that the second signal on the screen is the shear wave wave
Repeat the above steps 1, 2, 3, 4, and 5. Then: 1) With the first signal at 50mm on the screen, move the gate to the second signal on the time base. 2) Increase the gain until the signal is 80% screen height. 3) Adjust the velocity velocity until the sound path distance digit digital al display shows 50mm. 50mm. 4) Note that the velocity of this sound wave is that of a shear wave. The experiment can now be repeated with shear waves to show that this waveform is also hemispherical.
10
Compression and Shear Waves Travel Together The shear wave is a secondary motion of sound that is generated from the primary source of the compression at an interface, in solids only. The compression wave, after generating the first shear wave, passes through the solid at 6 KPS (in steel) until it strikes a surface of a different acoustic impedance (a back wall, crack or inclusion to name a few). When the compression wave bounces off the reflecting surface, it will lose some of its energy by creating another shear wave and a surface wave. This will keep repeating as the compression wave keeps bouncing, until the sound energy from all waves is absorbed into the material as heat energy. A shear wave cannot be maintained in any medium that has no shear strength (resistance to a sideward force) such as in gases and liquids. Surface waves are so rarely used they will not be covered in this book. Direction of Motion Direction of Propagation Surface Wave
Shear Wave
Compression Wave
Fig. 8 When the atoms in a solid are struck and compressed, the bonds that tie the molecules together drag neighbouring atoms inwards to fill the void. They are then followed by a rebound when the compressed atoms spring back. The movement of the atoms is illustrated in (Figures 8 to11).
©2008 Andrew Cunningham
11
The Practical Guide to Ultrasonic Testing In the Real World
Fig. 9
Fig. 10
Fig. 11
The compression wave radiates out from a point source on a surface over a hemispherical wave front (seen as a semi-circle on the cross section). The shear wave is created simultaneously and propagates at approximately approximately half th thee speed. The shear wave echoes will appear on the screen with lower amplitudes, between the 1st, 2nd and subsequent compression back wall echoes (Fig.12).
1
1) 2) 3) 4) 5) 6)
12
2
3
4
5 6
Fig. 12 First back wall echo compression wave. First shear wave due to mode conversion of the compression wave to a shear wave at the back wall. First shear wave that travelled to the back wall and then reflected. Second back wall echo compression wave. Repeat shear wave. Repeat shear wave.
Atoms laying equal distance apart in their natural state 1
2
1 2
3
3
4
5
4
compression
6
5
6
rarefaction
7
8
9
7 8 9
10
10
compression
11
11
12
12
rarefaction
13 14
15
16
13 14 15 16
17 18
17
19
18 19
compression
λ Wavelength
λ is
measured from peak to peak
Amplitude
Fig. 13 The compression is the gathering motion of the atoms and the rarefaction is the spreading motion of the molecules from their original position. The wavelength is a measured complete cycle from peak to peak (or between two points in the same state of deflection and motion).
Note: To allow visualization, the sinusoidal curve is drawn showing the deflection on the vertical axis, although the actual deflection is horizontal in the direction of travel (Fig. 13).
©2008 Andrew Cunningham
13
The Practical Guide to Ultrasonic Testing In the Real World
Quick Calculations of the Wavelength ( ) The wavelength is determined by the velocity of sound in the material, divided by the frequency (time interval between each cycle) of the probe. To express this as a formula is
=
v F
=
Sometimes expressed as
c F
Examples: To calculate values easily in your head, replace or round up the compression velocity from 5960000mm per second in steel to 6 kilometres per second, and transpose 4,000,000 cycles per second, for example, to 4 MHz.
Divide the velocity 6 km per second by the frequency of 4 MHz probe. = Velocity
÷ frequency
= 6 (x1, 000,000mm/sec) ÷ 4 (x1, 000,000 cycles/sec) = 6 ÷ 4 mm/cycle = 1½ mm/cycle Shear wave velocity of 3,240,000mm per second: replace with 3km per second and divide it by probe frequency, for example 4 MHz. = Velocity
÷ frequency
= 3 ÷ 4 = 3/4 mm Knowing the wavelength is said to be important. It is also said that the smallest defect that can be found is ½ , 0.1 0.1 of a , anything anything larger than than grain, grain, twice twice the grain size to 10 times times the grain size size (depending on who’s book you read). This may be confusing to the technician, when all the aforementioned are true to a point. The fact is that the smallest defect you can find is irrelevant. The critical statement is, “What is the biggest defect you can miss?” All the mathematical formulae in the world will never compensate for a poor scanning pattern or probe manipulation. Examples will be shown later.
14
Amplitude and Decibels A decibel is a unit of measuring sound intensity in logarithmic units. "Logarithmic" means that each decibel step represents a multiplication. For comparing voltage values, use the following formula:
output dB = 20 × log10 input 2 = 6.021 ≈ 6 dB 1
Example : 20 × log10
To double the amplitude of the signal, a gain of 6 dB must be added to the amplifier gain control. To halve the amplitude of an output signal, 6 dB must be subtracted. (Note that to double the power, which is related to the square of the voltage, you need only add 3 dB.)
Fig. 14
©2008 Andrew Cunningham
15
The Practical Guide to Ultrasonic Testing In the Real World
The Screen Display The modern flaw detector uses a rectified r ectified screen display, which means that all negative values are converted to positive, and all signal peaks extend upwards (Fig.15).
Fig. 15
100% 90% 80% 50%
20% 10% 00%
-2dB
-2dB
-6dB
-14dB
-6dB
20%
-14dB
10% -20dB
-20dB
Fig. 16
16
Table of dB steps
100% - 2 dB = 80% 80% - 4 dB = 50% 50% - 2 dB = 40% 40% - 4 dB = 25% 25% - 2 dB = 20% 20% - 6 dB = 10% 10% + 20dB =100% 10% + 6 dB = 20% 100% - 14dB = 20%
100% - 6 dB = 50% 10% + 14dB = 50% 50% - 6 dB = 25% The signal amplitude on the screen is the measure of the voltage that was generated by the piezoelectric crystal, which is energized by the returning sound wave. All amplitudes may be expressed in either dB or % of full screen height as they are linear to each other when compared to the reference amplitude (Fig. 16). 0° probe reference reflectors are usually 1st or 2nd back wall echo, using flat bottomed and round bottom holes of differing diameters. For shear wave and angle probes, the most common references are side-drilled holes of differing diameters or corner notches, with the received signal set to a reference height for a comparison to any defect reflecting signal.
©2008 Andrew Cunningham
17
The Practical Guide to Ultrasonic Testing In the Real World
The Ultrasonic Flaw Detector The ultrasonic flaw detector set has changed in appearance over the years. Long gone are the cathode ray tubes, vacuum tube, control switches and the large transistors. The modern ultrasonic digitized set has a liquid crystal display, microchip processor and press buttons. The design and parts have changed but the function is still the same, to send out a pulse of sound and measure the time and amplitude of the reflected sound (Fig. 17). PULSE GENERATOR
RECEIVER PREAMPLIFIER CONTROLS
AMPLIFIER
PULSE GENERATOR
PROBE RECEIVER PREAMPLIFIER
PROBE
ANALOGUE TO DIGITAL CONVERTER CONTROLS
X
Y
Y
LCD ANALOGUE AND DIGITAL SCREEN DISPLAY WITH
X SCREEN DISPLAY
CONTROL INFORMATION
Fig. 17 Analogue flaw detector detector with Cathode ray tube
Digital flaw detector with memory an andd Liquid crystal display
All though the following describes the design of the original UT flaw detectors (cathode ray tubes), modern L.C.D. versions have been designed to follow the same principle: A beam of light (a ray) travels through the x and y cathodes, panning across the screen at a constant speed. The mechanism that controls the panning speed is often known as the “clock”. As this clock speed is a constant, time can be measured from it. It is called the “Time base”. With no interference, the beam of light will travel across the screen in the X direction (horizontally) in a straight line (Fig. 18).
18
Y
X
Fig. 18 The light travels across the screen at a constant rate and is measured in microseconds. When we scan 3 dimensional objects, we refer to the time base in mm or inches. Applying a small current to the Y plates will pull the beam upward. Y
X
Fig. 19 An increase in probe output voltage will temporarily increase the upward deflection (resulting in a spike in the line (Figures 19 and 20). The height of the deflection is called amplitude. To measure the height of the deflection, we use decibels.
Y
X
Fig. 20
©2008 Andrew Cunningham
19
The Practical Guide to Ultrasonic Testing In the Real World
Positive + Negative - -
Screen RF mode Fig. 21 The R. F. (radio frequency) screen display (Fig. 21) shows the amplitude as it is measured, both negative and positive. The R.F. display is often used to display phase shift (shift of the peaks between left and right or negative and positive) which may occur when the ultrasonic beam hits the interface between dissimilar materials.
Fig. 22
Fig. 23
Converting the negative peaks to positive creates the “Full Wave Rectified” screen display (Fig. 22). Moving the rectified signal to the bottom of the screen gives room for amplification of the signal (Fig. 23).
Fig. 24 Fig. 25 A "Half Wave Rectified" screen display is created c reated by entirely removing either negative or positive peaks from the data (Figures 24 and 25). When positive peaks are removed, the remaining negative peaks are flipped up to the positive scale.
20
A fully digitized ultrasonic set with memory files and calculating functions is meant to make the ultrasonic examination more accurate, but it is a “double-edged sword”. Dependency by the technician on the automated functions may lead to inaccurate results as examination parameters change. For example, wear to the shoe of a shear wave probe will change the zero point (or delay); sensitivity and the exit point on the probe and may also change the beam angle. A digitized set will not correct these errors, but will simply give inaccurate results. Retrieving the calibration from the memory is easy, but that it not enough, the calibration must be checked each time before use. The gain control is used to manipulate the received electrical signal from the crystal. A change in the gain control changes the amplification of the incoming signal, but does not change the actual crystal output. To change the output of the crystal via the pulse generator, the voltage must be changed. In other words, turning the gain up does not make th thee crystal work harder or shorten its working life.
©2008 Andrew Cunningham
21
You have reached the end of this sample
Want to keep reading? You can buy this book at PageMasterPublishing.ca/Shop
To find more books by Canadian authors or inquire about publishing your own book, contact PageMaster at: PageMaster Publication Services Inc.
