Development Of  Characteristic Impedance Meter

M. Sivaramakrishna

doi:10.17577/IJERTV2IS50367

Volume 02, Issue 05 (May 2013)

Development Of Characteristic Impedance Meter

DOI : 10.17577/IJERTV2IS50367

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Authors : M. Sivaramakrishna
Paper ID : IJERTV2IS50367
Volume & Issue : Volume 02, Issue 05 (May 2013)
Published (First Online): 16-05-2013
ISSN (Online) : 2278-0181
Publisher Name : IJERT
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Development Of Characteristic Impedance Meter

M. Sivaramakrishna,

Indira Gandhi Centre for Atomic Research, Department of Atomic Enrgy, Kalpakkam, Tamilnadu, India

Abstract The paper describes the development of characteristic impedance meter. This is the first step towards automization of measurement of characteristic impedance of high frequency signal cables and connectors in Fast breeder reactors.

Index TermsCable, impedance, connector. For a list of suggested keywords, send a blank e-mail to sivarama@igcar.gov.in

INTRODUCTION

The paper is on the DEVELOMENT OF CHARACTERISTIC IMPEDANCE METER. The work is to

design the scheme & circuit for the meter and program it to display the characteristic impedance value of the cable connected to the terminals of the meter, especially in the light of non availability of meter for direct measurement of characteristic impedance of cables. Circuit is designed keeping in view of various options the user should be provided, like reset, test mode, voltage and frequency selection range etc. The paper details the simulation studies. A prototype is being developed based on the study.
Maximum power transmission principle is used to develop the meter. The power delivered by the cable is maximum when the cable is connected to a resistance equal to the cables characteristic impedance value. A voltage controlled resistor is used in the circuit, whose value is varied until maximum power transmission is achieved and the corresponding resistance value is displayed as characteristic impedance value of the cable. A microcontroller is used to calculate the power transmitted and to control the other peripheral devices like LCD, DAC and ADC. Annexure 1 gives the details of characteristic impedance in general industrial applications.
CHARACTRISTIC IMPEDANCE VALUES:

The earliest viable long-distance electrical communications system was the telegraph and its introduction spawned a whole range of new studies, techniques and products intended to

maximize its benefits and its efficiency. Characteristic impedance of the resulting transmission lines was 600 ohms. The characteristic impedance of a wire-pair transmission line, though a function of wire thickness, distance between the conductors and the permittivity of the insulation between the pair of wires, 600 ohms was widely adopted as the 'standard' for telecommunications systems and later broadcast studio installations. More modern multi-paired cables had characteristic impedance closer to 140 ohms. Given that characteristic-impedance only has significance where the cable distances are a significant fraction of the wavelengths of the signals being carried the cable runs in general didn't come close to the distances where characteristic impedance is an important factor. The introduction of digital technology, however, revived the importance of characteristic impedance as the cable now had to demonstrate a reliable and predictable performance at frequencies significantly beyond their analogue counterparts and are now operating with signal wavelengths closer to the run-lengths of the cables. Presently,

75 ohms coaxial are widely available in the market. The characteristic impedance of the cable often ranges from 50 to 300 ohms.
EXISTING METHODS FOR CHARACTERISTIC IMPEDANCE CALCULATION:
The design formula for characteristic impedance of a single coaxial line is:

Where:

Z0 = Characteristic impedance E = Dielectric constant (air is 1.0) D = Inside diameter of the "return" (outer) conductor (conductive metal tube or one or more braids) d = Outside diameter of the "go" (inner) conductor of coaxial cable

These formulae show that the characteristic impedance of any cable is directly determined by the conductor sizes, the spacing between them and the type of insulation used. Any change in these will affect the characteristic impedance.

An approximate value of characteristic impedance can be estimated by the formula Z0=sqrt (Z0c* Zsc)

Where Z0c is the impedance of the length of the cable with the far end open and Zsc is when the far end is shorted.

In the above figure, cable of characteristic impedance zero is short circuited. All of the transmitted power is reflected back from the shorted end, because none of it is absorbed by the load. The impedance in this case is measured to be Zsc.

The above figure the cable is left open. Even in this case all of the power is reflected because none can be absorbed by the load. The impedance in this case is measured to be Zoc.

When the cable is terminated in a resistor of characteristic impedance value, the combination acts as an infinite length cable. The signals travel down the cable and are not reflected.

Variation of characteristic impedance value with frequency: The impedance of real lossy transmission line is not constant, but varies with frequency. At lower frequencies, L<<R and C< <G. hence Zo=sqrt(R/G). At higher frequencies L>>R and C>>G, then the characteristic impedance is given by Z0=sqrt(L/C). Example: at 100 Hz , Z0=900 ohms and in 30- 40 Hz frequency range, 50 ohms.

The frequency dependence of characteristic impedance value should be considered while developing the meter.
DEVELOPMENT OF CHARACTERISTIC IMPEDANCE METER:

The increasing use of electrical pulses in the transmission of data by cable has resulted in a need for a better understanding of the electrical characteristics of a cable. In the high frequency region, it is a relatively simple matter to make the load resistive equal to the cable impedance. However, pulses are a mixture of low and high frequencies, depending on their rise time, duration, and repetition rate. It is up to the system designer to determine whether the rising impedance of the cable at low frequencies is going to cause any difficulty and to take whatever design steps may be necessary to allow for it. When an alternating voltage is applied to the cable, with the far end open, a current will flow. With voltage (E) and current

(I) measured in this circuit, impedance (Z) can be calculated (Z = E/I). The impedance will have some magnitude and some phase angle, which can be either positive or negative.

However, if a portion of the cable is cut off and the measurement is repeated, a different impedance magnitude and a different phase angle will be observed. The characteristic impedance (Z0) of a cable is independent of length, so obviously these measurements do not yield the characteristic impedance.

Many system specifications state the characteristic impedance value of the cables used. Any cable-maker's catalog will list the characteristic impedance values of most coaxial cables, which usually range from 50 to 95 ohms. The catalog may also refer to values of 100 to 200 ohms for certain shielded pairs which appear to be designed for special applications. But impedance information on the more common types of cables is not readily available to the cable user. This is because there are too many variations of the applications involved with the cables. The methods discussed earlier provide only an approximate value.

4.1 MAXIMUM POWER TRANSMISSION PRINCIPLE: Consider the circuit shown below. A cable (Z0) is connected to a power source with a resistance (ZL) in series.

By Ohms law and power definition, in the above circuit

By differentiating the above equation for maximum power, the condition obtained is Z0= ZL.

From the above graph, power transmitted initially increases with increase in the value of ZL, reaches maximum at Z0 and decreases ZL>Z0.

There is no device in the market presently that can give the characteristic impedance value directly. Moreover, methods mentioned earlier either give unreliable values or approximate values.

So based on the maximum power transmission principle, a meter is to be developed to measure characteristic impedance value up to 5 % accuracy.
4.5.1. Simulation:

In this paper, simulation software is used to simulate the circuit components. It is a layout package, which is used to create a PCB when the circuit has been designed. Schematic capture and interactive simulation software are used to create the circuit drawing and to test the circuit prior to building the real hardware. Mathematical circuit modeling system is done to get the real experience. Onscreen buttons and virtual signal sources, for example, provide inputs to the circuit. Output can be displayed on a voltage probe or on a virtual oscilloscope. With the microcontroller simulation, aprogram attached and debugged instantly.
Push button is used to RESET the meter. Toggle keys are used for hardware interrupts. As they produce level signals, differentiators are used to convert them to edge signals that can trigger interrupts in microcontroller. Four terminals are provided (two on each side)in the meter for the cable to be connected. The schematic shows the switch used to connect the sample cable in the test mode
PROGRAMMING THE MICROCNTROLLER: Microcontroller must be programmed to follow the sequence of steps required to calculate the characteristic impedance value of the cable. A source code can be attached to Microcontroller. is used to C language is used to write the main program.

5.1 PROGRAM FLOWCHART:

When the meter is connected to the mains, the circuit components should be checked if they are working properly. Checking the Microcontroller memory is necessary every time it is turned on. So a routine is included in the program to assign some value to each memory location and retrieve it to compare. On mismatch of the values, error message saying memory not working is displayed. All memory locations are initiated to zero to avoid random values. ADC-DAC working is also checked. By controlling the switch, ADC and DAC are connected. A digital value is given to DAC and the same is compared to digital output of the ADC. On mismatch, an error message is displayed on the LCD. If everything goes fine with the checking, the Microcontroller will proceed to calculate the characteristic impedance value. Below is the flowchart depicting the same:

START mode:

By pressing the start button and connecting the cable to the terminals provided, characteristic impedance value can be calculated. The voltage amplitude and frequency can be selected by changing the knob positions. The internal circuit changes accordingly (R1 value in the op amp square wave generator circuit). A message connect cable is displayed on the LCD. After the cable is connected, output of the DAC is used to vary the MOSFET resistance value(R). Voltage from ADC output is used to calculate the power delivered (V2/R). this is continued until maximum power is delivered and the corresponding value is displayed as Z0. The same is shown in the following flowchart:

TEST mode:

In the test mode, the inbuilt sample cable is connected instead of the external cable, using the switch. One of digital output of Microcontroller can control the switch. Thereafter the same operations are performed as discussed for START function.

RESET mode:

On pressing RESET, the program counter goes to the starting memory location. The calculation can be restarted by using this option. This is given high priority in the program, so on pressing reset microcontroller aborts the present operation and starts the process from the beginning.

Start

Test mode

Terminals are connected to inbuilt 75ohm test cable

Voltage= 1V, 5V, 10V

Frequency= 1MHz, 10MHz, 100MHz

Vary resistance and calculate power=v2/r

Z0=r when maximum power

Connect cable

Vary resistance and calculate power=v2/r

If Z0=75o

If maximum power is not achieved

hm

Z0

value

Z0 not in

Z0=r when maximum power transfer

Z0=75

ohms

Meter is not working

range

VOLTAGE CONTROLLED VARIABLE RESISTOR:

MOSFET is used as the variable resistance in the circuit. By applying a transverse electric field across an insulator (generally SiO2) deposited on the semiconducting material, the thickness and hence resistance of a conducting channel of a semiconductor material can be controlled. In enhancement MOSFET, application of electric field causes an increase in majority carrier density in the conducting regions.

A thin layer of a metal (aluminium) coated on the insulator acts as gate. By applying positive voltage to gate and grounding substrate, results in as electric field between drain and source. An inversion layer is formed by the minority charge carriers present in the substrate. As the positive voltage on the gate increases, the induced layer in the semiconductor increases and current flows from drain to source through it. Thus the conduction through the MOSFET is controlled by the gate voltage.

For proper functioning, the gate to source voltage (VGS) and drain current are suitably selected by biasing the MOSFET.

In the region before pinch off , where VDS is small, the drain to source resistance RD can be controlled by the bias voltage VGS.

Equations:

The resistance (RD) varies with voltage (VGS) according to the above equation, acting as a voltage controlled resistor. By using the above circuit in the meter, the resistance is varied until maximum power is transmitted and corresponding value is displayed as characteristic impedance of the cable. The code to run the system is given in the annexure 2.

5. SUMMARY:

An attempt is made to automize the measurement of characteristic impedance in nuclear instrumentation of fast reactors. A prototype will be made and qualified.

Ref:1. Wikipedia

Annexure 1

CHARACTERISTIC IMPEDANCE OF A CABLE:

Transmission line:

A transmission line is a specialized cable designed to carry alternating signals of radio frequency. These signals are of high frequency and their wave nature should be considered. Different cables are used as transmission lines depending on frequency and nature of he signal. Types of transmission line include coaxial cable, ladder line, wave guides, twisted pair etc. Wave guides are physical structures that guide electromagnetic waves in the optical spectrum. Common type wave guides include optical fiber, dielectric slabs which use the principle of total internal reflection. Twin lead cables have copper wire at a distance. These are used for parallel

transmission. Commercially manufactured twin lead is ladder line, used in balanced connection of antennas. Coaxial cable is considered as the main form of transmission line.

Coaxial cable: It is an electrical cable with an inner conductor surrounded by a flexible, tubular insulating layer, surrounded by tubular conducting shield. These are mainly used as feedlines connecting radio transmitters and receivers with their antennas, in computer network and distributing cable television signals. All these applications involve high frequency signal transmission, where small amount of reflections could distort the signal and may fail to serve its purpose.

Applicability of transmission line theory:

In many electric circuits, the length of the wires connecting the components can be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire.

The cable or wire is treated as a transmission line if the length is usually greater than 1/10 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behavior in systems which have not been carefully designed using transmission line theory.

Definition:

Characteristic impedance (Z0) of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections.

SI unit of characteristic impedance is the ohm.

The voltage and current phasors on the line are related by the characteristic impedance as:

Z0 =V/I

The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component (Z0 =

| Z0 | + j0). Characteristic impedance appears like a resistance in this case, such that power generated by a source on one end of an infinitely long lossless transmission line is transmitted

through the line but is not dissipated in the line itself.

A transmission line of finite length that is terminated at one end with a resistor equal to the characteristic impedance (ZL = Z0) appears to the source like an infinitely long transmission line. In this case Z0 corresponds to the input impedance.

Transmission line model:

ZL = Z0

line can transport, with higher frequencies being attenuated more than lower ones. The series and parallel resistances result in losses down the line, reducing the ability of the line to transport the signal power efficiently

Every transmission line consists of circuit elements distributed along its length. Because current flows through the conductors, the line has series inductance, and because there is always a return path, which is normally another adjacent conductor, it has parallel capacitance. The series inductance and parallel capacitance are the dominant elements in the equivalent circuit of lines, and are present even in theoretically perfect cases. But in real lines the conductors are not perfect, so they also have some series resistance, and the dielectric or insulation separating the two conductors is not perfect so it has some parallel resistance. The series and parallel resistance are less significant than the inductance and capacitance, unless there is a fault in the line.

The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:
1. The distributed resistance R of the conductors is represented by a series resistor (expressed in ohms per unit length).
2. The distributed inductance L (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (Henries per unit length).
3. The capacitance C between the two conductors is represented by a shunt capacitor C (farads per unit length).
4. The conductance G of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (Siemens per unit length).

In the real line the elements are distributed continuously along the line, and are not lumped at intervals along the length as shown.

In the above figure, each section of the equivalent circuit looks like a low pass filter, so the effect of the inductance and capacitance is to limit the bandwidth of the signals which the

The characteristic impedance is given by

Z0

Where R, L, G, C are the corresponding values per unit length and is angular frequency.

FOUR TERMINAL MODEL:

For the purposes of analysis, transmission line can be modeled as a two-port network (also called a quadrupled network), as follows:

In the simplest case, the network is assumed to be linear (i.e. the complex voltage across either port is proportional to the complex current flowing into it when there are no reflections), and the two ports are assumed to be interchangeable. If the transmission line is uniform along its length, then its behaviour is largely described by the single parameter characteristic impedance. Typical values of Z0 are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission.

When sending power down a transmission line, it is usually desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source. This can be ensured by making the load impedance equal to Z0, in which case the transmission line is said to be matched.

INFINITE LENGTH CABLE:

Definition – The characteristic impedance, Z0, of a line is the input impedance of an infinite length of the line.

The transmission line model of a cable can be simplified to an equivalent circuit by using boxes to represent each section, as shown below. The input impedance looking into the one end of this infinite line can be taken as characteristic impedance since the reflections are zero.

As the line is infinitely long, more sections can be added as shown below, without making any difference to its properties.

Since the length is still infinite, the input impedance is still the characteristic impedance.

The original line could be replaced by single impedance, Z0, as shown below, and the input impedance would be unchanged.

Therefore, if a finite length of line is terminated in its characteristic impedance, Z0, then its input impedance will also equal Z0 and it acts as infinite length line without any reflections.

Annexure 2:

PROGRAM CODE:

void DAC_Init(){ //

to connect to dac TRISD=0; //to declare portD as output port

TRISC3_bit=0; TRISC4_bit=0; TRISC5_bit=0;

TRISC6_bit=0; //four more output pins required for dac(12 bit) TRISB4_bit=0; //to WR pin of dac(declared as outputpin) TRISB5_bit=0; //to CLR pin of dac(declared as output)

TRISB6_bit=0; //to latch the dac(declared as output)

PORTD=0; //to give a value of zero

initially(lower 8 bits)

PORTC=0; //to give a value of zero

initially(upper 4 bits)

RB4_bit=1; //se WR pin

RB5_bit=1; // clear this bit to clear the dac

RB6_bit=1; //clear this bit to latch the value

}
void memory_check() { char temp=0,temp1=0; // variables declared to assign values and to retrieve values

FSR0=0;

do{

INDF0=FSR0;//assign the address value to the register

temp= INDF0; //retrieve the value from the memory

if(temp!=FSR0){ //compare the value to check Lcd_Init(); //to initialise lcd (connect the pins) Lcd_Out_Cp(" memory incorrect"); //display the memory is not working using built in lcd function break; //**command to halt the uc or go to

off mode

}

Else FSR0++;

} while(FSR0<=0xFF);

temp=0; for(FSR0=0xFF;FSR0<=0xFFF;FSR0++,temp++){//

after FSR0=0xFF, FSR0 cannot be assigned to the memory register

INDF0=temp; temp1=INDF0; if(temp1!=temp){

Lcd_Init(); //to initialise lcd Lcd_Out_Cp(" memory incorrect"); //display the memory is not working break; //**command to halt the uc or go to

off mode

}

} for(FSR0=0x00;FSR0<=0x3FF;FSR0++){

INDF0=0;//to initiate all the memory locations to zero

}

void dac_adc_check(){

ADC_init(); DAC_init(); RA2_bit=1; PORTD=0x088; if(ADRES!=0x88){

Lcd_Init();

Lcd_Out_Cp(" adc or dac not working");

//**command to exit from the program

}

}

int voltage;
int voltage_from_lookup_table(int resistance){

//luk up using table in memory TBLPTR= 0x266+resistance; // say 0x266 has voltage value for zero resistance, where the table starts

//**command to read frm memory TBLRD*;

//**read into TABLAT and increment voltage= TABLAT ; //get data

return voltage;

}
- int resistance_for_known_voltage(int voltage){
  
  // function to get resistance for voltage transmitted, for Zoc and Zsc
  
  int *ptr;
  
  int temp=0;
  
  int resistance;
  
  do{ temp++;
  
  ptr=0x266+temp;
  
  }while(voltage<=(*ptr)&& temp<=1000);
  
  if(temp>=1000){ //to check if Z is in the range of 10ohm to 1000ohm Lcd_Out_Cp(" ci is not in range"); //to declare Zoc or Zsc are not in the range
  
  //**command to exit //** to halt the program at this point
  
  }
  
  resistance=*ptr;
  
  return resistance; // return the value to assign it to Zoc or Zsc
  
  }
- ADC_Init(); // Initialize ADC module with default settings
- unsigned ADC_Get_Sample(unsigned short channel);
  
  //default function of adc to get analog value from the specified channel
- unsigned ADC_Read(unsigned short channel);
  
  //default functions in the library to get the digital value into a variable
- int adc_output_peak_voltage(){ //to get the peak voltage value to be used in power calculation int output_adc[30];
  
  int vnum=1;
  
  int temp;
  
  output_adc[0]=0; do{
  
  output_adc[vnum]=ADC_Get_Sample(7); temp=vnum-1; if(output_adc[vnum]<output_adc[temp]) output_adc[vnum]=output_adc[temp];
  
  }while(vnum<=30);
  
  return output_adc[30];
  
  }
- void latch_init(){
  
  RE0_bit=0; //to enable output of the latch
  
  RE1_bit= 1; //to select the latch
  
  }
  
  int voltage_frm_lukup_table(int resistance){ // luk up using pointers
  
  int *ptr; //declare a pointer
  
  ptr=0x266+resistance; //get the adress of the voltage required at ptr assuming tabular values start at 0x266 voltage=*ptr; //store the value at voltage variable return voltage;
  
  }
- void dac_output_voltage(int resis)(){ int voltag;
  
  voltag= voltage_frm_lukup_table(resis); PORTD=voltag;
  
  RC3_bit=voltag>>8; RC4_bit=voltag>>9; RC5_bit=voltag>>10; RC6_bit=voltag>>11;
  
  }
  
  //pins assigned to control switches
  
  // Lcd pinout settings
  
  sbit LCD_RS at RA4_bit;
  
  sbit LCD_EN at RA3_bit;
  
  sbit LCD_D7 at RD7_bit;
  
  sbit LCD_D6 at RD6_bit;
  
  sbit LCD_D5 at RD5_bit;
  
  sbit LCD_D4 at RD4_bit;
  
  sbit LCD_D3 at RD3_bit;
  
  sbit LCD_D2 at RD2_bit;
  
  sbit LCD_D1 at RD1_bit;
  
  sbit LCD_D0 at RD0_bit; sbit LCD_RS_Direction at TRISA4_bit; sbit LCD_EN_Direction at TRISA3_bit; sbit LCD_D7_Direction at TRISD7_bit; sbit LCD_D6_Direction at TRISD6_bit; sbit LCD_D5_Direction at TRISD5_bit; sbit LCD_D4_Direction at TRISD4_bit; sbit LCD_D3_Direction at TRISD3_bit; sbit LCD_D2_Direction at TRISD2_bit; sbit LCD_D1_Direction at TRISD1_bit; sbit LCD_D0_Direction at TRISD0_bit;
  
  int
  
  Zi;
  
  int
  
  Z0;
  
  int
  
  v;
  
  int
  
  temp1,temp2;
  
  unsigned
  
  int
  
  vcr,m;
  
  double power[100];
- void main() { Lcd_Init();

Lcd_Out_Cp("connect the cable"); //

start of the program RE0_bit=0; //to latch the lcd DAC_Init();

Zi=10;

do{

dac_output_voltage(Zi);

v =adc_output_peak_voltage() ; power[m]=(v*v)/Zi;

Zi++;

}while((power[Zi-2]>power[Zi-1])|| (power[Zi- 1]>power[Zi-3]));

RB6_bit=0; //to latch dac

Z0=Zi-3+10; //Zi-3+10 is the value of the impedance where maximum power transmissin occurs, +10 for series resistance Lcd_Init();

Lcd_Out(1,1,&Zi); // display characteristic impedance

}

void test_mode(){

RA0_bit=1; Lcd_Init();

Lcd_Out_Cp("test mode"); // start of the program

RE0_bit=0; //to latch the lcd DAC_Init();

Zi=10;

do{

dac_output_voltage(Zi);

v =adc_output_peak_voltage() ; power[m]=(v*v)/Zi;

Zi++;

*

}while((power[Zi-2]>power[Zi-1])|| (power[Zi- 1]>power[Zi-3]));

RB6_bit=0; //to latch dac

Z0=Zi-3+10; //Zi-3+10 is the value of the impedance where maximum power transmissin occurs, +10 for series resistance Lcd_Init();

if(Z0==75)

Lcd_Out_Cp("working normal, no error"); Else

Lcd_Out_Cp("error, test result not equal to 75");

}
void reset_mode(){

Lcd_Cmd(_LCD_CLEAR); // Clear Lcd display

main();

int		Zi;
int		Z0;
int		v;
int		temp1,temp2;
unsigned	int	vcr,m;
double power[100];

Development Of Characteristic Impedance Meter

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