2. REFERENCE. QD/HW/SPF/M/ Nov. 2002

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1 . REFERENCE This section contains tables, equations and general reference information frequently required by data acquisition engineers and in particular those in the aerospace industry. QD/HW/SPF/M/ Nov. 00 1

2 Contents Reference General Physical units and conversions...3 Bits, counts, and noise...4 Numbers and formats...6 PCM Codes...8 Frame Synchronization Patterns...9 Shunt resistor values 100Ω Shunt Resistor Table (Traditional Values) Ω Shunt Resistor Table (Linear Response) Ω Shunt Resistor Table (Traditional Values) Ω Shunt Resistor Table (Linear Response) Ω Shunt Resistor Table (Traditional Values) Ω Shunt Resistor Table (Linear Response) kΩ Shunt Resistor Table (Traditional Values) kΩ Shunt Resistor Table (Linear Response)...17 Thermocouple response tables J-type Thermocouple Tables...18 K-type Thermocouple Tables...0 E-type Thermocouple Tables...3 B-type Thermocouple Tables...5 R-type Thermocouple Tables...8 S-type Thermocouple Tables...31 T-type Thermocouple Tables...34

3 Decimal prefixes PHYSICAL UNITS AND CONVERSIONS 10 1 deca da 10-1 deci d 10 hecto h 10 - centi c 10 3 kilo k 10-3 milli m 10 6 mega M 10-6 micro µ 10 9 giga G 10-9 nano n 10 1 tera T 10-1 pico p peta P femto f exa E atto a Note: ACRA CONTROL use an upper case K for 104 (for example KBytes). Unless otherwise stated MByte means Bytes. Units of length The metric or International System (SI) unit of length is a meter (m) 1 kilometer 1km = 1000m Some conversions from Anglo-American units are 1 foot 1ft = 30.48cm 1 inch 1in or 1" =.54cm = 5.4mm 1 English mile 1M = 1609m = 1.6km 1 Nautical mile 1knot = 185m = 1.9km 1 mil 10-3 in = 5.4mm Units of temperature There are four popular units of temperature Celsius, Fahrenheit, Kelvin and Rankine. The conversion formulae to and from Celsius (sometimes called centigrade) are: Kelvin Celsius Celsius = Kelvin Rankine (Celsius ) x 9/5 Celsius = (Rankine x 5/9) Fahrenheit (Celsius x 9/5) + 3 Celsius = (Fahrenheit-3) x 5/9 Some examples are: Celsius Fahrenheit Kelvin Rankine Absolute zero C F 0K 0 Rank Melting point of water 0 C 3 F 73.15K Rank Boiling point of water 100 C 1 F K Rank 3

4 BITS, COUNTS, AND NOISE An analog to digital converter (A/D) with one bit can count 0 to 1. In general the number of counts of an n-bit A/D is given by: Counts = n For the 1-bit A/D, each count value represents 50% of the span of the A/D. In general for an n-bit A/D, each count represents the following percentage of the span: % = = 100 n Counts Similarly the resolution of an A/D, in parts per million (ppm), can be calculated using: ppm = 10 6 n The dynamic range of an A/D can be calculated using the following formula: Range db = resolution 0 log = 0 log span 10 ( n ) 6.0 n Assuming every value is equally likely to appear at the input to the A/D, the quantization error is between ±r/. The square of the error is between 0 and r/4, the average value of which is r²/1. The root of the average value of the error squared is r/square root 1. For example, a 1-bit A/D with an input range of ±10V has a resolution of 4.88mv and a quantization noise of 1.407Vrms. The maximum signal to the A/D is ±10V, so the signal-to-noise ratio for the 1-bit A/D is: 10 0 log = 77.03dB 4

5 Bits Counts % Ppm Dynamic range (db) Signal/Noise (db) , , , , , , , , , Reference:"INFORMATION TRANSMISSION MODULATION AND NOISE" Mischa Schwartz; McGraw-Hill International Editions 5

6 NUMBERS AND FORMATS The table below illustrates how hexadecimal, octal and binary coded decimal digits are represented in binary. It also lists (for completeness only) the first 16 Gray codes. Binary (Bin) Hexadecimal (Hex) Binary Coded Decimal (BCD) Octal (Oct) A B C D E F 1000 Gray code For example, the number 365 (decimal) can be written in the following ways: BCD HEX 16D OCT Note: For large numbers BCD requires more bits. To convert Hex or Oct to binary convert each digit using the table above. To convert from binary to Hex (Oct) start at the least significant bits (LSBs) to the left and arrange them in groups of four (three) and use the table above. 6

7 There are three popular ways of representing negative numbers as illustrated below for a four-bit analog-todigital converter with a ±8V input range: Voltage In Sign plus magnitude Offset Binary 's complement ± N/A Note: Offset Binary starts at the lower end of the range and counts from there. As such it can readily be used for non-symmetrical ranges. To convert from offset binary to 's complement (or vice versa), invert the most significant bit (MSB). To convert from binary to 1's complement invert each bit. 7

8 PCM CODES At first glance it may appear that representing a logic 1 with one level and a logic 0 with another would be as good a way as any to transmit data (this is called NRZ-L and is illustrated below). However unless a clock is also transmitted there may be problems with transmitting long patterns of 1s (or 0s). For example, if due to Doppler effects or oscillator drift there is a 10% uncertainty, the receiver cannot be sure if it has received 9, 10 or 11 consecutive bits. Also long patterns of 1s (or 0s) may appear as a dc signal, which may be difficult to retrieve from a tape recorder. One popular solution is to ensure a transition in the center of each bit (such as with BIφ-L below). However this requires extra bandwidth in the data channel. Another popular method is to try to ensure a continuous pattern is unlikely to occur using a "randomizer" circuit as illustrated for RNRZ-L below. However this means that one bit received incorrectly may cause three bits to be decoded incorrectly RZ RNRZ-L x 4 Return to Zero 1 level 1 for the first half of the bit only 0 level 0 throughout the bit Random Non-Return to Zero-Level *Care must be taken with BIφ-M(S) and DBIφ-S(M). In the 1996 and 1993 versions of IRIG-106 both pairs of codes were included. However after 1996 DBIφ-M is to be referred to as BIφ-S and DBIφ-S is to be referred to as BIφ-M. **Delay modulation is sometimes referred to as Miller Code 8 BIφ-L BIφ-M (before 1996) BIφ-S (before 1996)* DBIφ-M (before 1996) BIφ-S (after 1996)* DBIφ-S (before 1996) BIφ-M (after 1996)* DM-M DM-S Bi-Phase-Level 1 change from level 1 to level 0 at the center of a bit 0 change from level 0 to level 1 at the center of a bit Bi-phase - Mark 1 change of level at the start and in the center of the bit 0 change of level at the start of the bit only Bi-phase - Space 1 change of level at the start of the bit only 0 change of level at the start and in the center of the bit Differential Bi-phase - Mark (before 1996) Bi-phase - Space (after 1996) 1 change of level at the center of the bit only 0 change of level at the center and at the start of the bit Differential Bi-phase - Space (before 1996) Bi-phase - Mark (after 1996) 1 change of level at the center and at the start of the bit 0 change of level at the center of the bit only Delay modulation - Mark** 1 change of level at the center of the bit 0 change of level at the start of the bit if the previous bit was 0 Delay Modulation - Space** 1 change of level at the start of the bit if the previous bit was 1 0 change of level at the center of the bit

9 FRAME SYNCHRONIZATION PATTERNS In Pulse Code Modulation (PCM) systems a pattern is often used to identify the occurrence of a frame. In particular with IRIG-106-Ch. 4, a SYNCWORD appears at the start of every MINOR frame. At first glance, it may appear that for a given number of bits one pattern is as likely to occur as any other. However if the link is open all 1s (or 0s) might be received or in the presence of oscillations or "non-zero memory" patterns may repeat for example " " or " ". The problem of finding optimum patterns in noisy "non-zero memory" systems was addressed by Barker and the following patterns are sometimes referred to as "Barker Codes". LENGTH CODE (Bin) CODE (Hex) B B D D A EB E6A CD CCA E DE D DC C DA A E FA F F DC E9 ACC D F5E EBC CD DBC CD F37 D F E6B F74E 9498 Note: The convention followed by ACRA CONTROL as default is that the leftmost bit is the first transmitted bit. 9

10 100Ω SHUNT RESISTOR TABLE (TRADITIONAL VALUES) The shunt values in this table are those most commonly used for strain gage calibration. However the output voltage versus µω/ω response is non-linear. With today's acquisition systems (better than 10-bit resolution) pseudo errors appear. The values are given here for completeness only. The linear-response values on the next page are those recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

11 100Ω SHUNT RESISTOR TABLE (LINEAR RESPONSE) The shunt values in this table produce a linear response (output voltage versus µω/ω) and as such are the values recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

12 10Ω SHUNT RESISTOR TABLE (TRADITIONAL VALUES) The shunt values in this table are those most commonly used for strain gage calibration. However the output voltage versus µω/ω response is non-linear. With today's acquisition systems (better than 10-bit resolution) pseudo errors appear. The values are given here for completeness only. The linear-response values on the next page are those recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

13 10Ω SHUNT RESISTOR TABLE (LINEAR RESPONSE) The shunt values in this table produce a linear response (output voltage versus µω/ω) and as such are the values recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

14 350Ω SHUNT RESISTOR TABLE (TRADITIONAL VALUES) The shunt values in this table are those most commonly used for strain gage calibration. However the output voltage versus µω/ω response is non-linear. With today's acquisition systems (better than 10-bit resolution) pseudo errors appear. The values are given here for completeness only. The linear-response values on the next page are those recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

15 350Ω SHUNT RESISTOR TABLE (LINEAR RESPONSE) The shunt values in this table produce a linear response (output voltage versus µω/ω) and as such are the values recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

16 1KΩ SHUNT RESISTOR TABLE (TRADITIONAL VALUES) The shunt values in this table are those most commonly used for strain gage calibration. However the output voltage versus µω/ω response is non-linear. With today's acquisition systems (better than 10-bit resolution) pseudo errors appear. The values are given here for completeness only. The linear-response values on the next page are those recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

17 1KΩ SHUNT RESISTOR TABLE (LINEAR RESPONSE) The shunt values in this table produce a linear response (output voltage versus µω/ω) and as such are the values recommended by ACRA CONTROL (see TEC/NOT/00). How to use the table: Ω is the shunt resistance required to produce a 1100µΩ/Ω deflection. µω/ω *open*

Lab 2: Measurements and the Metric System

Lab 2: Measurements and the Metric System The word measure means to determine the size, capacity, extent, volume, or quantity of anything, especially as determined by comparison with some standard or unit.