Precision-Video-Cables-Part-1

Precision Video Coaxial Cables, Part 1: Impedance Page 1 of 5 Belden Electronics Division, 2002Precision Video Coaxial Cables Part 1: Impedance Martin J. Van Der Burgt Senior Product Engineering Project Manager Belden Electronics Division Abstract: Over the years, engineers have come to identify coaxial cables typically in one of two ways: either by impedance or RG-type. The impedance refers to the characteristic ornominal impedance of the cable. Recently, somemanufactures have begun to specify tighterrequirements on the cable. This paper willexamine the nature of characteristic impedance and to what extent the values are relevant . Characteristic Impedance: A signal travels, or propagates, through a transmission line. Therefore, its behavior is defined by thepropagation constant. ) )( ( CjGLjRj ω ω βαγ + +=+= (1) Where:γ is the propagation constant α is the attenuation constant β is the phase constant R is the resistance L is the inductanceG is the conductanceC is the capacitancef = frequency in Hertz ω= 2πf = radian frequency The signal can be described in many ways to better understand its properties and behavior.The natural approach is to divide the signal intovoltage and current. By knowing the properties of the dielectric material in the transmission line, we can then determine the intrinsic impedance.Thus, a positively traveling current wave isrelated to a positively traveling voltage wave bythe intrinsic impedance ωεσωµηjj += (2) Where:η is the intrinsic impedance µ is the permeability σis the conductivity εis the permittivityThe intrinsic impedance is analogous to the characteristic impedance, Z 0. Characteristic impedance is a more common term made up ofvalues we often see associated with coaxialcable: Resistance, Inductance, Capacitance, andthe lesser known Conductance. ) () ( 0CjGLjRZωω ++= (3) Solving the characteristic impedance formula results in the curve and simplification formulas shown below. GRAPH 1 At high frequencies, typically greater than 1 MHz, the coaxial cable will approach the “steadystate” value that is referred to as the nominal or typical impedance. This is the value stated by most manufacturers as the characteristicimpedance. Therefore the common expression used to identify the characteristic impedance of a coax is: dD CLZ ln21 0εµ π== (4) and is also simplified to: =∗=dDVp VpCZ log100138101670 0 (5) Precision Video Coaxial Cables, Part 1: Impedance Page 2 of 5 Belden Electronics Division, 2002Where: D is the diameter over the insulation d is the diameter of the conductor C is the Capacitance (pF/ft)Vp is the Velocity of Propagation (%) All of these formulas will provide a good approximation of the high frequency characteristic impedance of a coaxial cable. Traditionally, cable manufacturers have specified this value as typical or nominal. In some cases,the value had a tolerance. In the case of videocable, a typical value was 75 ± 3 ohms. Therefore, the characteristic value is between the value of 72 and 78 ohms or about ± 4%. Someprecision video cables, such as Belden 8281,made with a solid conductor and solidpolyethylene dielectric were specified as ± 1.5ohms, or ± 2%. Recently, manufacturers have begun to tighten this impedance tolerance. This is due mainly tothe use of statistical process control and theinfiltration of automation into the manufacturing process. These improvements allow the cable manufacture to more consistently meet the 75ohm target. While some manufactures try to usethis specification as a selling point or technicaladvantage, it must be remembered that this is thenominal impedance of the cable and does not account for the true impedance variations within the cable. The graph below illustrates this point. This is an impedance trace of Belden 1505A PrecisionVideo Cable. Notice how the impedance follows the theoretical characteristic impedance (red line), but that the actual impedance does havevariation (blue line). GRAPH 2 Belden 1505A is specified as 75 ± 1.5 ohms and does meet the requirement as shown in thisgraph. It is also obvious that the impedance at individual frequencies is not within the characteristic value tolerance. So, what then is the value of a tight characteristic impedancetolerance? Input Impedance: Input impedance is the term used to describe the impedance at any given specific frequency. The term vector impedance is also sometimes used. Unfortunately, this impedance is not uniform at all locations and all frequencies within the cable.After all, this is the REAL world! Therefore,what is really happening within a cable can be best understood (and measured) by looking at the reflection coefficient. When signal traveling in a coax encounters an impedance mismatch, a portion of the signal will be reflected back to the source. This reflected signal has magnitude and phase and is measuredas the reflection coefficient. 01 0201 02 ZZZZej +−=Γ=Γφ (6) Where:Γis the reflection coefficient φis the phase angle By measuring these signal reflections we can determine what is happening within the coax. We can calculate the actual mismatches . We can also look at the input impedance with respect to frequency and length using thereflection coefficient. This formula is written interms of the impedance variation within the transmission line. ljZZljZZZZ LLinββ tantan 00 0++= (7) Where: Z in is the input impedance Z0 is the characteristic (or reference) impedanceZ L is the load impedance at a specific location βtanis the tangent of the phase angle l is length The input impedance, Z in, is represented in the GRAPH 2 as the blue line. Z in represents specific1505A Impedance Magnitude 6570758085 01 02 03 04 05 06 07 08 09 01 0 0 Frequency (MHz)Ohms Precision Video Coaxial Cables, Part 1: Impedance Page 3 of 5 Belden Electronics Division, 2002impedance at specific lengths. Length equates to wavelength equates to frequency. Therefore, impedance variation at specific frequencies can be measured. This will more accurately predictthe electrical performance of the cable. An extreme example of this can be shown with a cable that has an excellent characteristic impedance value (red line), but has terrible impedance variation within the cable (blue line).This cable, too, meets the same requirement asthe previous example, 75 ± 1.5 ohms. GRAPH 3 The characteristic impedance value is important because the cable must be as close to 75 ohms aspossible to minimize reflective losses. But it ismore critical that the variation of impedance around the nominal be minimal. This is why impedance is important. Impedance mismatchescause signal reflections. So, again the question, what then is the value of a tight characteristic impedance tolerance? It would seem that the characteristic impedancevalue alone will not guarantee the performancelevel of the cable. Rather it is primarily aspecmanship issue. Note also that the characteristic impedance value is a magnitude only measurement, while the reflection coefficient and input impedancemeasurements both include phase. Why Magnitude Only: Because of the high frequency characteristic impedance properties, a magnitude only measurement allows for simplified calculations and measurements to beused to represent the relative characteristics ofthe cable. These include TDR (Time DomainReflectometer) impedance, calculated per MIL-C-17G, and calculated per the simplified formulas.Also, a closer look at the input impedance equation (7), will show that the phase angle should be near zero in a “good” cable. This isbecause when you divide a complex number, youactually subtract it. Assuming that the angle isabout the same in both parts of the equation, theend result should be a phase angle about zero degrees. Using our equations for reflection coefficient (6) and input impedance (7), lets look at theimpedance phase with the assumption that thecable has reasonably low impedance variation. These assumptions reveal that the impedance phase will be less than ± 20 degrees as can beseen in GRAPH 4. GRAPH 4 x: Reflection Coefficient Phase y: Reflection Coefficient Magnitude z: Impedance Phase Reflection coefficient for reference .20 = 14db RL = 1.5:1 VSWR .15 = 16.5db RL = 1.35:1 VSWR .10 = 20db RL = 1.22:1 VSWR.05 = 26db RL = 1.11:1 VSWR .00 = infinite RL = 1.0:1 VSWR Here we can see that as the reflection magnitude nears zero, so does the impedance phase. Also,the larger the reflection coefficient magnitude, the more effect the reflection coefficient phase has on the impedance phase. So, to minimizeimpedance phase, the reflection coefficient mustbe minimized. This means there must be minimalimpedance variation within the cable. The input impedance formula does not “limit” the variation or value of the impedancemagnitude the same way it does the phase.Therefore, we can have a much wider variationImpedance Magnitude with Periodic Impedance Discontinuities 6570758085 0 100 200 300 400 500 600 700 800 900 1000 Frequency (MHz)Ohms Precision Video Coaxial Cables, Part 1: Impedance Page 4 of 5 Belden Electronics Division, 2002of impedance magnitude as a result. Using the same assumptions, the impedance magnitude can vary ± 30 ohms as can be seen in GRAPH 5. Here we see as the reflection coefficient magnitude approaches zero, the impedancemagnitude approaches its characteristic value of75 ohms. Also, the lower reflection coefficient magnitude, the less effect reflection coefficient phase has on the impedance. GRAPH 5 x: Reflection Coefficient Phase y: Reflection Coefficient Magnitude z: Impedance Magnitude Minimizing the reflection coefficient magnitude is the key. Here we truly see that a minimumreflection coefficient magnitude means that thecable should be very near its characteristicimpedance. So, a perfect cable with minute impedance variations will have minimal reflectioncoefficient and will be at its characteristicimpedance value. However, a cable withexcellent characteristic impedance can still have impedance variance of ± 30 ohms. So, again the question, what then is the value of a tightcharacteristic impedance tolerance? Actual Cable Measurements: If we apply this theory and put it together with frequency, what will the values be? This data is measured from 300 kHz to 3.0 GHz using a network analyzer from a randomlychosen spool of Belden 1505A. The samplelength is 100 feet.GRAPH 7 Notice that the impedance grass is about +/- 3 ohms and that the characteristic impedance isabout 74.8 ohms. GRAPH 8 Notice that as we predicted, the impedance phase angle is near zero. Note: This data was collected using a 2.5GHz S- parameter test set. Actual values above 2.5 GHzmay not be correct. As we can see from the actual data, our theory holds true. The impedance magnitude is centered around the characteristic value and the phase isnear zero. This explains why manufactures reportthe characteristic impedance magnitude only. Itfurther shows that the actual tolerance of theimpedance at any given frequency will be greater than the characteristic impedance tolerance value. (The tolerance is the “grass” around thebest-fit-line value.) Magnitude and Phase Together: Since both impedance magnitude and phase can be affected within the cable, it makes sense to look at both to determine the true performance of the 1505A Impedance Magnitude 6570758085 0 500 1000 1500 2000 2500 3000 Frequency (MHz)Ohms 1505A Impedance Phase -5-2.502.55 0 500 1000 1500 2000 2500 3000 Frequency (MHz)Degrees Precision Video Coaxial Cables, Part 1: Impedance Page 5 of 5 Belden Electronics Division, 2002cable. What measurement and specification will do this best? This will be discussed in more detail in Part 2 of our technical series. Specmanship: So, how tight can the characteristic value be held? Given excellent manufacturing practices, materials, productdesigns, SPC implementation, measurement andoperator capabilities, the standard deviation for characteristic impedance will be 0.5 ohms or less. Belden uses a 6-sigma approach when setting specifications to guarantee the customer that ourproducts will meet or exceed expectations. In statistical terms, this means that the CpK is greater than 1.33 or that more than 99.9934% ofproduct falls within the specification limits. Thus for characteristic impedance, we specify +/- 3 standard deviations which will be: Ohms5.15.033 ±=∗±=±σ Belden’s tolerance for characteristic impedance for precision video cables is 75 +/- 1.5 Ohms.(Belden products 8281, 1855A, 1505A, 1694A,7731A, and others.) Given our historical test lab data on this cable, most cable is within 75 +/- 0.75 ohms. This willbe further illustrated in Part 2. Conclusion: Characteristic impedance is not a true representation of the performance and/or quality of a transmission line. This was best illustrated in GRAPH 3. This cable has had aperiodic discontinuity introduced into the cable.(A slight compression at 10 foot intervals.)Notice that the input impedance shows thedefect, but characteristic impedance does not. A TDR measurement may show some of the defects, depending on how far into the cable youlook, but the resultant value may not. Therefore, the characteristic impedance value alone – or it’s tolerance – does not tell the whole story of cable quality or performance. A specification for impedance variation, bothmagnitude and phase, is required to demonstratethis capability. This will be the topic of part twoin this series.Part 2: In our next paper, the use of the reflection coefficient will be discussed, using the measurements of Return Loss, Voltage Standing Wave Ratio, and Structural Return Loss to guarantee cable performance and minimizeimpedance variations within the cable. About the Author: Martin J. Van Der Burgt Marty is a Senior Product Engineering Project Manager for Belden Electronics Division. His experience encompasses project managementand product development positions. Hecurrently has responsibility for all design anddevelopment efforts, and manages the day-to-dayactivity of product engineers, for Belden’s entertainment, service provider, and industrial product areas. Marty received his Bachelor ofScience Degree in Electrical Engineering(BSEE) from Marquette University, Milwaukee,WI in 1992 and has been with Belden since that time. He is a member of several professional organizations and standards bodies, and has hadseveral articles on Audio/Video and RF topicspublished in trade magazines: most recently, aco-authored tutorial on “High-Definition Cablingand Return Loss” in the January 2001 SMPTE Journal. Marty also holds a FCC Amateur Extra Class amateur radio license. He and his wifeBeth live in Richmond, IN. Marty Van Der Burgt Graphs and data formatted by Carl W. Dole.