# RF RADIATED EMISSIONS MEASUREMENT SYSTEMS TUTORIAL

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2 Electromagnetic measurement systems are used to measure power densities, or power spectral densities, of electromagnetic fields at a point in space. Power density is defined as the "power per unit area normal to the direction of propagation usually expressed in units of Watts per square meter W/m 2 ), or for convenience in units such as milliwatts per square meter (mw/m 2 ), or even in microwatts per square centimeter (µw/cm 2 )." Plane-waves, power densities, electric field strengths (E), and magnetic field strengths (H) are related by free space loss, i.e., 377 ohms (Ω ). Electric field strengths and magnetic field strengths are expressed in units of Volts per meter (V/m) and Amperes per meter (A/m), respectively. Field strength is therefore defined as: E = Square Root (120πP) E = rms value of field strength in Volts/meter P = power density in watt/meter = impedance of free space in ohms Power density (P D ) is related to the electric field strength (E) and the magnetic field strength (H) as: P D = E 2 2 (far field) /377Ω = 377ΩH Again, the rate at which electromagnetic energy (power) is propagated by a wave - - power density -- is usually specified in Watts per square meter (W/m 2 ). The power density equation is: P D = P T /4πr 2 P D = power density in watts/meter 2 P T = transmitted power in Watts r = distance in meters Radiated electromagnetic fields -- radiated emissions -- are produced from many sources. Sources of electromagnetic energy range from manmade sources such as commercial broadcast stations and automobile ignition systems to natural sources such as galactic noise and lightning. To further complicate matters, these emissions can drastically differ in frequencies and in their magnitudes. Because of the potential wide range of measurement requirements special measurement systems are sometimes necessary. These systems must be well-planned or inaccurate measurements may result. Important design specifications should include system selectivity and system sensitivity. These terms will be defined and demonstrated in the following sections.

4 The power received by the antenna is then defined by: P r = PA e = PGλ 2 /4π (Watts) P = power density in Watts/meter 2 G = antenna (power) gain λ = wavelength in meters also, Combining these equations with the field strength equation yields: then, Knowing that: since an antenna factor is defined as: P r = E 2 Gλ 2 /480π 2 P r = V r 2 /Z o V r = received voltage Z o = receiver input impedance V r 2 /Z o = E 2 Gλ 2 /480π 2 λ = 300 meters/second/f (MHz) E = (V r fπ/50ω)(square Root (30/Z o G)) we can simplify and rearrange terms to yield: K = E/V r then, K = (fπ/50ω)(square Root(30/Z o G)) or in logarithmic form [for Z o = 50 Ω (ohm) system]: K = 20log 10 f MHz -G db (db) THE RECEIVER AND AMPLIFIER A receiver is an electro-mechanical device that receives electromagnetic energy captured by the antenna and then processes (extracts) the information, or data, contained in the "signal."

8 Note: Noise figures and noise factors are different ways of specifying noise. In this text, noise factors will be used to describe linear ratios, and noise figures will be used to describe logarithmic ratios. Again, a receiver's selectivity, the ability to select frequencies or frequency bands, is chiefly dependent on the receiver's tuner design, which is mainly the function of the receiver selection. Because receiver system sensitivity presents one of the greatest challenges, sensitivity will be addressed in detail. For simplicity, a spectrum analyzer will be used as the receiver for this discussion. We will first determine the receiver's sensitivity from its indicated power level. The indicated power level of a spectrum analyzer is essentially the base-line trace observed on its cathode-ray tube (CRT) display, usually expressed in dbm. It may be more useful to convert this unit (dbm) to a more useful unit such as dbv. In a 50Ω system this conversion is done by adding 107 db to the indicated power level displayed on the analyzers CRT display. As an example, an indicated power level of -90 dbm (on the CRT display) is equivalent to an electric plane-wave of 17µV. Note: The 107 db factor is only applicable in 50Ω systems. FIGURE 3. SPECTRUM ANALYZER DISPLAY Converting the receiver's sensitivity into a plane-wave field strength equivalency, ambient field strength reference at the antenna, is not difficult but may be confusing at first because of the unit conversions and the concept of equivalent field strengths. As shown above, it may be easier to first convert the receiver's indicated sensitivity power level (dbm), to a plane-wave equivalent voltage (dbµv). After this conversion, the

9 equivalent field strength sensitivities can be easily calculated in units of dbµv/m or V/m. This conversion can be accomplished using "antenna factors." The antenna factor (db/m) when added to the indicated sensitivity level (dbµv) of the receiver will produce the equivalent field strength sensitivity referenced at the antenna (dbµv/m), referenced to an isotropic antenna. For example, an indicated field strength of 17 dbµv plus an antenna factor of 25 db/m is equal to a field strength of 42 dbµv/m. Because the antenna factor does not include any losses such as cable losses and filter losses, these losses will have to be accounted for to accurately calculate equivalent field strengths or field strength sensitivities. For ease in calculating, these losses (in db) can be added to the antenna factor. This resultant number, when added to the indicated receiver sensitivity, in dbµv, will yield an equivalent ambient field strength or electric plane-wave sensitivity. Note: This will only be true for a particular antenna at a specific frequency. Each antenna factor will be different for each measurement frequency. Using the following measurement receiver (spectrum analyzer) system specifications as an example: System Specifications: 1. Receiver sensitivity (indicated) = -90dBm 2. The antenna factor at MHz = 25 db 3. The cable loss at MHz = 2 db By performing the following steps the measurement system's plane-wave equivalent sensitivity, in dbµ V/m, would be: Step 1. First, converting the indicated receiver sensitivity level from a power (dbm) to an equivalent voltage (dbµv), assume a 50Ω system, would yield: S R = -90 dbm db = 17 dbµv Step 2. Correcting for cable losses and antenna factors, the system sensitivity (S e ) would be: S e = 17 dbµv + 25 db/m + 2 db = 44.0 dbµv/m Step 3. By taking the antilog of the sensitivity level calculated in step 2, the equivalent, or effective, plane-wave electric field strength sensitivity (S e) in µv/m will be: S e = 44.0 dbµv/m = 10 ((44.0dBµV/m)/20) = µv/m

10 THE RECEIVER, PRE-AMPLIFIER, AND ANTENNA SYSTEM SENSITIVITY Now that the sensitivity of a receiver system with just an antenna has been defined, the sensitivity of a measurement system including a pre-amplifier will be explained -- without the use of antenna factors. This will be slightly more complicated than a measurement system containing only a receiver and an antenna. Again, the system's sensitivity will be defined as the minimum ambient signal level, power density, or field strength that the system can detect or measure referenced at the receive antenna. To determine the overall system sensitivity the total system's noise factor must be calculated using the noise factors of each active device within the system. If the manufacturer of each device has not specified these parameters they can be measured and/or calculated. To calculate the system noise factor the following equation is used when a preamplifier is included in the measurement system: NF s = NF 1 + ((NF 2-1)/G)) NF s = noise factor of the system NF 1 = noise factor of the preamplifier NF 2 = noise factor of the receiver G = Gain of the Preamplifier (Power) Because antenna factors will not be used, there are two other parameters that will be needed to complete the overall system sensitivity calculations, the measurement frequency must be defined and the antenna gain must be known. The frequency is important because the effective capture area (A e ) of the antenna must be known. This calculation is based on the equation λ 2 /4π; Lambda (λ) being the emission wavelength specified in meters. The antenna gain is important because it obviously affects the system's sensitivity. To make the system sensitivity calculations easier, logarithmic expressions will be used in most cases. Again, noise figures will be used to express noise factors in logarithmic form. The system sensitivity (S e ) of the measurement system can be calculated using the following: S e = N fig -174 * +B r -A e (dbw/m 2 ) N fig = system noise figure (db) B R = receiver bandwidth, in Hertz (db)

11 A e = antenna effective capture area (db) * = 10 log 10 Boltzman's Constant x 290 K + 30 db As an example, the following will demonstrate how to calculate the system's sensitivity (S e ) using the following device parameters: Device Parameters: 1. Receiver I-F Bandwidth = 9 khz 2. Receiver Noise Figure = 15 db 3. RF Preamplifier Power Gain = 26 db 4. Preamplifier Noise Figure = 4.15 db 5. Measurement Frequency = 635 MHz First, the receiver sensitivity (S R ) is equal to: S R = 15+(-228.5) = (dbw) = (dbm) (For convenience in later comparisons, dbw was converted to dbm. You will notice (later) the difference between the receiver sensitivity and the ambient system's sensitivity.) Next, we must calculate the system noise figure (N fig ). This will be more complicated because we must obtain the answer in logarithmic form from calculations performed using a linear approach: 1. NF 1 = 4.15 db=10 (4.15/10) = NF 2 = 15 db=10 (15/10) = G = 26 db=10 (26/10) = NF 3 =2.6+((31.6-1)/398)=2.68 then, N fig = 10log = 4.3 db The effective capture area of the antenna, A e, will now be calculated as follows (for unity gain antenna): 1. λ= 300 m/s frequency (MHz) = 300 / 635 =.47 meters 2. A e = λ 2 /4π =.472 / (4 x ) =.0176 meters 2 = 10 log = db The receiver bandwidth (B R ) calculation will be: 1. B R = 10 log 10 Frequency (Hz) (power bandwidth) 2. B R = 10 log Hz = 39.5 db

12 Finally, using equation S e = N fig -174+B r -A e, we can calculate the total system sensitivity. The system sensitivity (power density) will be: S e = (-17.5)= dbm/m 2 Now that the system sensitivity (S e ) is known, defined in power density units (dbm/m 2 ), it may be more useful to convert further to more commonly used units such as field strengths. Again, the units of measurement for field strengths are Volts per meter (V/m), or for convenience dbµv/m (decibel ratio of V/m referenced to 1 microvolt). For ease in understanding, and for simplicity in calculating, it is recommended that unit changes be done by first converting power densities (dbm/m 2 ) to milliwatts per square centimeter (mw/cm 2 ), then converting to field strength units such as V/m or dbµv/m. In converting power densities to field strengths the following conversion factors will be helpful: 1. Units/cm 2 (square centimeters) = units/m 2-40 db 2. Volts/meter (V/m) = Square Root (mw/cm 2 x Ω) Using the above conversion factors (1 and 2), the equivalent field strength sensitivity would be: dbm/m 2 = dbm/cm dbm/cm 2 = 10 (-152.7dBm/10) = 5.4 x mw/cm 2 3. Square Root (5.4 x mw/cm 2 x Ω) = 1.4 x 10-6 V/m 4. 20log x 10-6 V/m = 2.9dBµV/m Some additional helpful conversion factors for radiated measurement units are: dbw/m 2 = dbv/m-25.8 dbw/m 2 = dbµv/m dbm/m 2 = dbµv/m dbm/cm 2 = dbµv/m dbm/cm 2 = dbv/m-35.8 dbw/m 2 = dbm/m dbw/m 2 = dbw/cm dbw/m 2 = dbm/cm The measurement system's sensitivity has now been calculated and defined. It is important to note, however, that the system may not be capable of measuring all ambient signal levels down to this level. As mentioned earlier, ambient noise levels may be higher than the measurement system sensitivity. This will result in the ambient noise levels masking potential measurements down to these levels. These potential problems can be resolved with proper system pre-selection (RF input filtering) and receiver I-F bandwidth adjustments.

14 The overall system sensitivity will thus be dependent on the noise figure of the selected receiver, the noise figure and gain of the preamplifier (if used), the system cabling losses, and the gains of the selected antennas. For high-gain systems, used for measuring low signal levels, extreme caution should be taken to ensure that the combination of the antenna gains and amplifier gains will not produce signal levels that exceed the maximum input levels allowed for the selected receiver. Again, because of the importance, saturating an amplifier or a receiver's input stage may create intermodulation products and may result in inaccurate measurements. REFERENCES Brench, C.E., "Antenna Differences and Their Influences on Radiated Emission Measurements," Paper presented at the 1990 IEEE Interference Symposium on EMC. Duff, W.G A handbook on mobile communications. Don White Consultants, Inc. Hewlett Packard. Spectrum Analyzer Series. Application Note Kraus, J.D Antennas, 2nd ed. New York: MGraw Hill. Nahan, N.S., Kanda, M., Larsen, E.B., Crawford, M.L., Methodology for standard electromagnetic field measurements. IEEE transactions on instrumentation and measurement. IM-34, No. 4 (December) Society of Automobile Engineers EMC antennas and antenna factors: how to use them. Aerospace Information Report (January).

15 Useful example and formulas:

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