Conformity Magazine - April 2008 - (Page 27)

where Pd is the power density at r meters and P is the radiated power. Power density Pd and electric field are also related, as: Pd = E2 / Z0 where E is the electric filed in V/m and the Z0 is free space impedance (Z0 =μ / ε =120 π , Ω). Combining these two equations, and relating E with P3, we get: E2 = 120 π P / 4 π r2 or E2 = 30 P / r2 E= sqrt (30 P) / 3 (E-field at r = 3 meters) The radiated power appears as electric field E given by Equation 8 at r-m from antenna. The standard measurement distance for most EMC purposes is 3 m. Thus, rewriting Equation 8 in terms of power, we get: P = E2 r2 / 30 P = 0.3 E2 (P in W, and E in V/m at 3 m from antenna) In dB it can be written as: P (dBm) = 20 log E (dB μV/m) - 95.3 (9) (8) Pr = P3 Gr λ2 / (4 π r)2 (transmit antenna gain is implicit in P3) In a more general form, the power received can be written with both transmit and receive antenna gains as: Pr = Pt Gt Gr λ2 / (4 π r)2 (10) Pt is radiated power from antenna with no gain information, and Gt and Gr are the gains of the transmit and the receive antennas. If we assume an ideal isotropic system, then both Gt = Gr =1 Generally, for a simple dipole antenna, the value of gain is 1.62. Pr in watts is resulting power at r meters from the source, which is transmitting P3 watts. In logarithmic terms, this equation can be written as: Log (Pr) = - 22 + 10 log (Pt) + 10 log G1 + 10 log G2 + 20 log λ – 20 log r (11) Measurement Methods and Regulations – Some Examples In the following paragraphs, we shall consider a few examples of some SRDs/LPDs operating in different frequency bands, and try to correlate the specified limits expressed in various terms (e.g., conducted power, EIRP, ERP, E-field). We will compare the limits allowed between different standards/ Equation 9 is standard equation between power and electric field, but which power from Figure 1: P2 or P3? Some standards suggest it is P2, but we will investigate that later in this article. If we place another antenna in the space at some distance r from the radiating source, the power received by the antenna depends upon antenna effective area and the power density in the field. The antenna effective area, Aeff, is given by: Aeff = G. λ2 / 4π where G is the antenna gain. Combining equations for power density with effective antenna area, we get Friss’ transmission equation between two antennas; the power received Pr by receiving antenna is: Pr = Pd . Aeff = (P3 / 4 π r2 .)( Gr. λ2 / 4π) April 2008 Conformity 27 http://www.kikusui.us http://www.kikusui.us

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Conformity Magazine - April 2008 NewsBreaks Editor’s Note Mandatory Analog Cellular Service Ends FCC Releases Quarterly Reports on Consumer Inquiries and Complaints New Standards List Released for The EU’s Low Voltage Directive FDA Issues Notification on Unretrieved Device Fragments FDA Offers Guidance on Waivers for In-Vitro Diagnostic Devices ESD Open Forum Emerging Issues in Standards Challenges in Testing Design Fundamentals Focus on... New Products Product Reviews Premarket Approval Application Guidance Issued by FDA New Jersey Enacts Electronic Waste Recycling Regulations A New U.S. Standard for Workstation and Computer Design Might the CPSC Hold Retailers Accountable for Safe Products? CPSC Loses “Sole Toy Tester” CPSC Actions in the News IEC Standards Update UL Standards Update Telcordia Standards Update From Our “You Can’t Make This Stuff Up” Department Looking Back: Items from Past Issues of Conformity Advertisers

Conformity Magazine - April 2008

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