You know about coaxial cable (Fig. 1). We all use it in one form or another, and it seems simple enough. But while modern cable products are better than ever, there are some real subtitles in their selection and application.
Connecting dc and low-frequency ac including audio is easy. You just run some wires from point A to point B. The biggest challenge may seem to lie in choosing the right connector (see “Coax Connectors”).Your main concern, though, is resistance over the longer runs as well as high-power or high-voltage signals. Frequency doesn’t usually enter into it. But try that with signals with frequencies over a few hundred kilohertz, and weird things start to happen.
At these frequencies, the inductance and capacitance of the cables begin to come into play. The serial inductance and shunt capacitance form a distributed low-pass filter. The cable begins to store energy and delay the signals applied to it, not to mention attenuate them. The cable becomes a transmission line with very specific characteristics.
A cable doesn’t act like a transmission line until it is more than 0.1 ? long at the frequency of operation. For example, one wavelength at 450 MHz is:
? = 984/fMHz in feet
? = 984/450 = 2.19 ft
0.1 ? = 0.1(2.19) = 0.219 ft or about 2.63 in.
At this frequency, a pair of conductors over 2.63 in. long will have the characteristics of a transmission line.
The basic characteristic of a transmission line is that the cable will act like a complex impedance (R ± jX) to a signal source unless it is terminated in its characteristic impedance (ZO). The characteristic impedance (sometimes called surge impedance) of a transmission line is a function of the inductance (L) and capacitance (C) per foot or other unit of length or:
ZO = v(L/C)
ZO is a pure resistive value. An infinite length of the transmission line will appear to be a resistance equal to ZO to a signal source. Terminating any other length of line with a resistive load equal to ZO will appear to be a resistive load of ZO to a generator.
If the transmission line isn’t terminated in its characteristic impedance, the generator will see a complex impedance that is a function of its length. In addition, an improperly terminated transmission line will produce reflections. Signals not absorbed by the load are reflected back down the line toward the generator producing standing waves.
Standing waves are stationary variations of voltage and current along the line. These standing waves are the sum of the incident or transmitted signal and any reflected signal not absorbed by the load. In a matched line or one properly terminated, the voltage and current along the line is constant. Standing waves are undesirable, as they can cause signal distortion (for pulses), losses, and excessive voltages or current.
Coax cable is an ideal interconnection medium because it is self-shielding. The electromagnetic wave that propagates down the line stays entirely within the cable, except for some leakage where the shield isn’t solid. Solid foil shields do a better job than braid. But there are coax cables with two or more shields to ensure no signal leakage.
Unlike twisted pair, coax signals do not produce nor are they subject to cross talk and other coupling problems. Coax keeps noise and stray signals out and the desired signal in, meaning you can run coax cables directly parallel to one another or with twisted pair without interference.
The primary specification of a coax cable is its ZO. The most common value is 50 O, with 75 O also widely used. Most wireless and test applications use 50-O cable. Cable TV and VIdeo uses 75-O cable. Other available impedances are 93 and 125 O, but they aren’t as common. The impedance is set by the physical nature of the cable—specifically, the inner and outer conductor dimensions, their spacing, and the dielectric constant (e) of the insulating medium.
Voltage standing-wave ratio (VSWR) is an important factor in applying coax, but it is not a specification as such. It is usually calculated as:
VSWR = ZO/ZL or ZL/ZO
depending on which proVIdes a value greater than one. ZL is the load resistance. VSWR is actually the ratio of the maximum peak voltage to the minimum voltage along the line. It is related to the reflection coefficient (G), the ratio of the reflected voltage VR to the incident voltage VI:
G = VR/VI
The ideal G is 0. VSWR is calculated using the reflection coefficient: VSWR = (1 + G)/(1 – G) The ideal VSWR is 1, but many applications can tolerate mismatches with VSWR as high as 2 or 3 without excessive power loss. Figure 2 relates VSWR to power lost due to reflection.
The velocity factor (VF) is one more common parameter. It is the ratio of the propagation of the signal in the cable to the speed of light. Also, it is a function of the dielectric constant of the insulating material:
VF = 1/ve
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For coax, the VF is usually in the 0.6 to 0.9 range. Table 1 shows the most common dielectrics used in coax and the velocity factors. The VF affects the length of a wavelength of a cable. One wavelength is:
? = 984/fMHz
One wavelength of coax is:
? = 984(VF)/fMHz
Capacitance per foot is another common parameter. It too depends on the dielectric constant. The typical range is from about 6 to 31 pF per foot. Note that the lower the dielectric constant, the lower the capacitance per foot and the lower the decibel (dB) loss in the cable.
One especially important specification in high-power applications, the maximum voltage rating, is usually given as the RMS value of the maximum voltage rating. It ranges from 1000 to 15,000 V. Be sure to know the maximum peak value (1.414 × RMS) of the signal to be transmitted to ensure you are within the safety range.
If you know that there is a mismatch involved from cable ZO to load, then to determine the approximate effective value of voltage involved, multiply the actual input voltage by the square root of the expected VSWR. Incidentally, some coax also carries dc. The maximum dc voltage that can be applied is about three times the ac voltage maximum.
Time delay is an inherent characteristic of any transmission line, as it takes a finite amount of time for the signal to propagate through all that inductance and capacitance. That time delay (tR) shifts pulses and produces phase shifts in sine waves. It is a function of the dielectric constant:
tR = 1.016 ve ns/foot
One of the most critical specifications of coax is its attenuation, which is usually stated in dB power loss per foot. Specifications are sometimes stated as dB/100 feet or as dB/100 meters. Of course, that value increases with the frequency of operation.
When high frequencies and long lengths are involved, the cable represents a major loss of power. For example, a common RG- 58A/U cable has a typical attenuation of 5.3 dB per foot at 100 MHz. That is a loss of –0.53 dB/foot. If you put 100 W into this cable, you will get out only 29.5 W. That is a massive loss of 70.5 W in the cable itself. Attenuation is critical. For a given application, your job is to select the cable that will have the lowest possible loss—and keep the cable as short as possible.
A trend in wireless today is to locate the transmitter and/or receiver at the top of the antenna tower to avoid high transmission line losses. To achieve a desired output power, the designer has to produce a more expensive higher-power transmitter to compensate for cable loss. Tower-top electronics has gotten easier with smaller and lighter components, but it is still an issue in the cellular business where the need to climb towers for maintenance and repair and wind loading are still big problems.
A coax cable is a long low-pass filter whose cutoff frequency decreases with length (Fig. 3). But you can use coax well up into the gigahertz region. This is where waveguide is normally used. Yet for short runs of cable, coax is a reasonable design solution. Just watch the attenuation figures and select the lowest-loss coax you can find. Lengths of coax from a few inches to a few feet are practical at frequencies up to about 50 GHz. Generally, the larger the diameter of the cable, the lower its attenuation—but also the lower the operating frequency.
SELECTING A CABLE
There are thousands of different cable sizes and types. The most common ones are designated with the letters RG. The RG standards came out of World War II. RG means radio guide, and the U suffix often attached to the RG designation means universal. The RG standard is no longer used, and different RG numbers will probably have different specifications from manufacturer to manufacturer. Militaryspecification coax cable has an M17 designation. The standard is MIL-DTL-17H. The international standards with the IEC are 60096 and 61196.
A good choice is to stay with the popular and common types of cable, as they are widely available from multiple sources and cost less than some of the specialty cables (Table 2). The primary application will determine the most important specifications. Other important cable specifications include operating temperature range, the outside diameter of the cable, and the weight of the cable in pounds per foot.
Also, consider the environment, such as rain, wind, and ultraviolet exposure, as well as if cable flexing is involved. Coax does not flex well. Examine the manufacturer’s specifications and applications carefully.
As its name implies, hard line is coax that isn’t flexible like regular coax cable. It’s essentially a pipe within a pipe whose outer conductor can be up to several inches in diameter. Keep in mind that hard line isn’t waveguide, though. It truly is coax cable, but it’s designed for high power and low loss at UHF and low microwave frequencies. It is widely used for radio and TV broadcast antenna feeds and cellular basestations.
Most hard line is made with a solid copper outer shield with a solid copper inner conductor that may also be a small tube. The dielectric insulation between the two may be a foam polyethylene, air, or pressurized gas like nitrogen. The gas keeps the interior of the line dry since moisture may collect and attenuate the signal in most pipes. When air or gas is used, plastic or nylon spacers are used internally to keep the spacing between the conductors stable and consistent.
A good example of the latest type of hard line is the Cellflex series of cables made by Radio Frequency Systems (Fig. 4). They’re available in diameters of 0.5, 0.875, and 1.625 in. The center conductor is a copper tube, and the outer conductor is a corrugated aluminum tube. The corrugation makes the tubing bendable.
The dielectric is polyethylene foam with a VF of 0.90 and a capacitance of 22.9 pF/ ft. The impedance is 50 O. As for specs, the 0.875-in. cable is usable up to 5 GHz. The attenuation at 1 GHz is a low 1.28 dB/100 ft. Power rating is 2.53 kW at that frequency.
Coax has been around for decades. With its continuous improvement over the years, it is still the connecting link of choice for RF and video. Fiber-optic cable may be making continuous inroads of its own, but for now, coax is still king.