Training A Oscilloscope Coaxial Cable 6October2010 Nishina School

Training A Oscilloscope, Coaxial Cable 6/October/2010, Nishina School, Hiroaki Ohnishi ( Advanced meson science lab. ) Reference: http: //www. hucc. hokudai. ac. jp/~a 10863/Co-axial%28 Rev 1. 5%29. pdf

Purpose for this training course • You have already learn from the lecture “Basic of Detector” done by Dr. Taketani that the idea of the detector for experiment, for example…. . However, no yet discussed how to treat electric pulse from the detector For this lecture, we will learn following two items • How to transfer the signal? • How to read it out? here Copy from Dr. Taketani’s presentation

Purpose for this training course (2) • Pulse (signal) need to be transfer out from detector (PMT) using something – Coaxial cable • Signal need to be read out using something – for example Oscilloscope… Oscilloscope is basic but very important tool for electronic test instrument that allows signal voltages to be viewed. From this training, we will learn basic usage for the Oscilloscope Coaxial cable is very important item to transfer the signal. From this training, we will learn basic property of coaxial cable.

Oscilloscope Typical signal shape from PMT • What is really happing inside? – Horizontal axis of the display indicates time information of signal – Vertical axis shows Voltage information for the signal at the timing If we want to measure signal like Vy(t) = cos(q), we will induce this signal in Y direction of the Oscilloscope, together with Signal you want Vx(t) = t – π to measure Signal in X direction. Then we will see signal shape on the screen. Time-to-position conversion signal

coaxial cable Waveguide: the term waveguide may refer to any linear structure that conveys electromagnetic waves between its endpoints. Coaxial cable is also a kind of waveguide. Electric field Magnetic field Impedance of coaxial cable, m 0 : permeability of free space e 0 : permittivity of free space a : diameter of inner conductor b : inner diameter of outer conductor You will be able to produce same impedance coaxial cable if you keep ratio “b/a”. Question: I brought two different type of cables (think and thick cables). Try to measure ratio “b/a” by yourself

Coaxial cable Key words (1) – Impedance matching When we proceed experiment at Lab. , we often discuss about the word “impedance matching”. What is “impedance matching”? I E Register R Ω Internal register rΩ • Try to calculate power consumption for this circuit. W= Model E 2 = (r+R)2 R E 2 (r-R) d. W d. R = (r+R)3 i. e. Maximum power transfer can be achieved if we set outer register “R” with equal to the internal register “r” of the source. I 2 R To send signal from source to detector, we always need to take care about impedance matching situation to maximize efficient power transfer. ( i. e. minimum energy loss ) Where is the lost power goes? Signal reflect back to the source Reflection

Coaxial cable (2) • Key words (2) – Signal reflection Impedance Z 1 Impedance Z 2 Vt, It Vi, Ii Vr, Ir GV (1+G)V = Vt Z 2= Vt = Vi+Vr Ii - Ir Vi/Z 1 -Vr/Z 1 It Case-1) if Z 2=0 Z 2 -Z 1 G= Z 2+Z 1 = - 1 Vt = (1+G)V Case-2) if Z 2=Z 1 Signal termination Z 2 -Z 1 G= Z 2+Z 1 = 0 No reflection Case-3) if Z 2=∞ Z 2 -Z 1 G= Z 2+Z 1 =1 Vt = (1+G)V = 2 V Vr Z 2 -Z 1 Vi = Z 2+Z 1 = G Reflection coefficient If we connect two path with same impedance, Z 1 = Z 2, then we expect no reflection in electrical circuit. Possible problem of reflection signal = reflection signal will not be able to distinguish with real signals. (possible source of fake signals…)

Coaxial cable (3) • Key words (3) – signal divider • Now we know what is “impedance matching” and how important it is. Sometime, we want to divide single signal to two signals Now, impedance of the coaxial cable is 50 Ω. Simplest way to divide signal is just split it something like, 50Ωcable Z = 50Ωcable You will be able to produce impedance matched signal splitter adding 3 registers as follows 50Ωcable rΩ 50Ωcable Impedance is not matched, Why? ? ? rΩ rΩ 50Ωcable Z = 25Ω 50Ωcable Question : Please calculate appropriate value of register “r” to satisfy impedance matching condition.

Coaxial cable (4) • Attenuator Now we know that we will use coaxial cable as signal transfer line to detector readout system, like oscilloscope. Following situation will be happened frequently. 1) Maximum voltage for the signal we want to measure is about 10 V. 2) However, maximum accepted voltage for readout system (oscilloscope) is only upto 5 V. We want to reduce maximum pulse of the signal down by half of original one, What we should do? What is most simple way to it with satisfied impedance matching condition? R 2 Amount of attenuation is denoted with 50Ω R 1 50Ω Oscilloscope d. B unit (decibel) a=10 x log 10 (“Input pulse heigh”/”output pulse height”) Example; If we want (“Input”/”output”)=2 situation, we need to choose 3 d. B attenuator Now we introduce new parameters, K=10 a/20, Z= impedance of the system K+1 2 -1 Z Z , R 2= R 1=Z x 2 K K-1 Question: try to check impedance matching condition in case of 6 d. B attenuator.

Impedance of coaxial cable m 0 : permeability of free space e 0 : permittivity of free space mr : permeability of dielectric er : permittivity of dielectric 2 a 2 b a : diameter of inner conductor b : inner diameter of outer conductor Impedance of coaxial cable can be written by Electric field Magnetic field You will be able to produce same impedance coaxial cable if you keep ratio “b/a”.

Example; List of cables which you will be able to purchase from company “Fujikura” a b a : diameter of inner conductor b : inner diameter of outer conductor If we take typical value of er =2. 1, please calculate impedance of those cables, when you have a time

What we will do during training -1 (1) Switch ON Oscilloscope 1) Connect pulse generator 2) Display pulse on screen and change • time range • Voltage range • Change trigger threshold 3)Try to change pulse from pulse generator to changing setting for pulse generator and repeat what you did in task 2). Pulse generator Oscilloscope

What we will do during training -2 (2) reflection measurement? ? ? 1) 2) 3) Connect pulse generator to oscilloscope with “T” connector Connect long cable to “T” connector Then check the signal on screen with 1) 2) 3) Open end of long cable 50 Ω　termination just short circuit it Pulse generator Oscilloscope T connector

What we will do during training -3 (2) Measurement of the speed of signal transfer in the cable ? ? ? 1) 2) 3) 4) Connect pulse generator to oscilloscope with “T” connector Connect 5 m cable to “T” connector Open end of long cable. Measures time distance of the signal and reflected signal. That is the time need to transfer signal along with 5 mx 2 cable. Therefore V=10 m/DT = ? ? ? Pulse generator Oscilloscope T connector

What we will do during training -4 (2) Measurement of the cable length by Oscilloscope 1) 2) 3) 4) Connect pulse generator to oscilloscope with “T” connector Connect unknown length of cable to “T” connector Keep open end of long cable. Measures time distance of the signal and reflected signal. Previous task you should know velocity of signal in cable as XXXX cm/ns. So, now you can estimate “cable length” from time distance. Please measure length of long cable. Pulse generator Oscilloscope T connector

What we will do during training -5 (2) Attenuator, signal splitter etc. 1) 2) 3) 4) 5) 6) Connect pulse generator signal to signal splitter. Connect both output of signal splitter to Oscilloscope CH 1 and CH 2. Compare signals Plug out CH 2 and connect it to Attenuator. send signal from Attenuator out put to Oscilloscope CH 2 then try to see signal difference between CH 1(signal before Attenuator) and CH 2(signal after) to change attenuation value on attenuator Pulse generator Splitter Oscilloscope CH 1 CH 2 Attenuator

Oscilloscope, Coaxial Cable – – Oscilloscope is basic but very important tool for electronic test instrument that allows signal voltages to be viewed. Example? • If someone want to count number of beta decay in the radioactive source, like 90 Sr which is famous radioactive source, what we should do? 1) Place the source on scintillator with photomultipler tube(PMT). ( Probably you have already leaned those words, scintillator and PMT from Dr. Taketani’s lecture) 2) Scintillator will convert signal of beta decayed electron to photons (light ), and those photon signal will be converted to electrical signal by PMT. 3) Then finally role of oscilloscope and coaxial cable comes in. Signals from PMT will be transferred by “coaxial cable” to “Oscilloscope” then we will be able to see the signal of beta decay from radioactive source by eye.

http: //www. hucc. hokudai. ac. jp/~a 10863/Coaxial%28 Rev 1. 5%29. pdf

Coaxial cable (2) • Key words (2) – Signal reflection Impedance Z 1 Impedance Z 2 Vt, It Vi, Ii Case-2) if Z 2=∞ Z 2 -Z 1 Vr G= Z 2+Z 1 ~1 = Vi i. e. Vr = Vi String wave reflected with closed end Case-1) if Z 2=0 Vr Z 2 -Z 1 G= Z 2+Z 1 = - 1 = Vi Vr, Ir Z 2= Vt = Vi+Vr Ii - Ir Vi/Z 1 -Vr/Z 1 It Vr Z 2 -Z 1 Vi = Z 2+Z 1 = G Reflection coefficient i. e. Vr = -Vi String wave reflected with open end Case-3) if Z 2=Z 1 Z 2 -Z 1 G= Z 2+Z 1 = 0 No reflection If we connect two path with same impedance, Z 1 = Z 2, then we expect no reflection in electrical circuit. Possible problem of reflection signal = reflection signal will not be able to distinguish with real signals. (possible source of fake signals…)