5/4/2005 Antenna Impedance present 1/1 Jim Stiles The Univ. of Kansas Dept. of EECS D. Antenna Impedance An antenna, like any other microwave device, has an input impedance. Although there are typically no resistors used antenna designs, an antenna impedance better have a real (resistive) component! HO: Antenna Impedance Antenna resistance has two components; the most important of which is the radiation resistance. HO: Radiation Resistance Given that antennas are not perfectly efficient, we find that a more useful, applicable, and measurable parameter than directivity is antenna gain. HO: Antenna Gain11/29/2006 Antenna Impedance 1/4 Jim Stiles The Univ. of Kansas Dept. of EECS Antenna Impedance Q: Is the radiated power equal to the available power (TxP)of the transmitter? A: Ideally it is! If TxradPP≠, then some power is being wasted. However, the perfectly ideal case of TxradPP= is not possible. As a result, we find that radP will always be less (at least a little) than the available power TxP. However, we find for well-designed antenna that radP will be very close to available power TxP. Q: Why isn’t the radiated power equal to the available power of the transmitter? What happens to this available power? A: One of two things, either: 1. Power is reflected at the antenna. 2. Power is turned to heat in a lossy antenna. Tx TxradPP< TxP 0Z11/29/2006 Antenna Impedance 2/4 Jim Stiles The Univ. of Kansas Dept. of EECS GUMZ Let’s consider the first phenomenon first. Power is reflected at the antenna if the antenna impedance AZ is not matched to the transmission line. Q: Antenna impedance? Does an antenna have an impedance? A: An antenna is a one-port device—every one-port device has an impedance! The antenna impedance acts as the load at the end of a transmission line. If 0AZZ≠ , then power will be reflected, and the power delivered to the antenna (AP) will be less than the transmitter available power: Thus, all the available power is delivered to the antenna only if its impedance is: 00AAZZ=⇒Γ= Q: Huh?? Characteristic impedance is a real value. If 0AZZ=, then the antenna impedance is purely resistive. Wouldn’t a resistor make a particularly bad antenna? Tx ()21AATxPP=−Γ TxP 0Z AZ 0AΓ≠11/29/2006 Antenna Impedance 3/4 Jim Stiles The Univ. of Kansas Dept. of EECS A: A resistor actually would make a particularly lousy antenna. Yet, the impedance of an ideal antenna is purely resistive. Æ These statements are not contradictory! Remember, a real load can absorb incident energy, whereas a purely reactive load cannot. For a reactive impedance, all incident power would be reflected—a purely reactive AZ would result in 0AP= . Thus, it is imperative that the impedance of an antenna have a real component if we wish for it to absorb energy, with maximum power transfer occurring when 0AZZ=. The difference between a resistor and an antenna, however, is what it does with this absorbed power. * A resistor will convert its absorbed power into heat. * An antenna will (ideally) convert its absorbed power into a propagating, spherical, electromagnetic wave! Tx 0AP= TxP 0Z AZ 1AΓ=11/29/2006 Antenna Impedance 4/4 Jim Stiles The Univ. of Kansas Dept. of EECS In other words, an antenna dissipates its absorbed power by radiating it into space. Q: So does this mean that an antenna will reflect no power? A: Generally speaking, antenna impedance will posses both a real and reactive component: AA AZRjX=+ Thus, we find antenna impedance—like all other antenna parameters—is frequency dependent. Q: So how do we eliminate (or at least minimize) the reflected power?? A1: Design the antenna such that 0ARZ=(e.g., 50Ω, 75Ω and then operate at a frequency ω such that 0AX= . A2: Implement a matching network! Tx TxP 0Z Matching Network 0AΓ≈11/29/2006 Radiation Resistance 1/5 Jim Stiles The Univ. of Kansas Dept. of EECS Radiation Resistance Q: Does all the power absorbed by AR get radiated (i.e., is radP equal to AP)? A: Generally speaking, no! Remember, there were two reasons why radiated power radPis less than the available transmitter power TxP. 1. Power is reflected at the antenna. 2. Power is turned to heat in a lossy antenna. From the first reason we have already determined that: ()21AATxPP=−Γ But because of the second reason we find that: AradPP< Ideally, all of the power delivered to the antenna (AP) is radiated (rad APP= ). However, antennas are made of materials with finite conductivity. Therefore they exhibit Ohmic losses!11/29/2006 Radiation Resistance 2/5 Jim Stiles The Univ. of Kansas Dept. of EECS In other words, most of the absorbed power is radiated, but some of the absorbed power is converted to heat. Thus, we find absorbed power consists of two components: ALradPPP=+ where: Power delivered to the antennaPower converted to heatRadiated PowerALradPPP=== Now, the power delivered to the antenna is the power absorbed by the antenna resistance AR. We can likewise divide this resistance into two components: ALradRRR=+ so that: AL AradZRR jX=++ where: Ohmic Loss ResistanceRadiation ResistanceLradRR11/29/2006 Radiation Resistance 3/5 Jim Stiles The Univ. of Kansas Dept. of EECS * The radiation resistance is defined such that radiated power is equal to the power absorbed by radR. * The Ohmic loss resistance is defined such that the power converted to heat is equal to the power absorbed by LR. Using our basic circuit theory we find: ()22122AAAALradVVPRRR==+ 22LLLVPR= 22radradradVPR= And from KCL: LLrad radLA A A AradLA L Arad radRRRRVVVVVVRR R RR R== ==++ Combining the above: 2222222222 222 2LAALLLLALLA AA AradAArad rad radAradAAAArad radVVVRRRPPRRR RR RVVVRRRPPRRR RR R⎛⎞== = =⎜⎟⎝⎠⎛⎞== = =⎜⎟⎝⎠ + VA - + VL - + Vrad - RL Rrad11/29/2006 Radiation Resistance 4/5 Jim Stiles The Univ. of Kansas Dept. of EECS Note then, as expected: LradLAAradAALradAAALradAAAAAARRPP P PRRRRPRRRRPRRPRP+= +⎛⎞=+⎜⎟⎝⎠⎛⎞+=⎜⎟⎝⎠⎛⎞=⎜⎟⎝⎠= Thus, rearranging the above results, we can determine resisitances LR and radR: LLLA L AAArad radAArad radAARPPP RRRPRPPP RRRP⎛⎞ ⎛⎞=⇒=⎜⎟ ⎜⎟⎝⎠ ⎝⎠⎛⎞ ⎛⎞=⇒=⎜⎟ ⎜⎟⎝⎠ ⎝⎠ Now, we define antenna efficiency as: antenna efficiencyradAPeP==11/29/2006 Radiation Resistance 5/5 Jim Stiles The Univ. of