In miniature receiver design, such as keyless entry and security devices, one challenging task is optimizing all circuits affecting radiated sensitivity. This important receiver parameter is difficult to predict, due mainly to noise matching, differing antenna configurations, and noise from nearby microprocessors.

However, it is possible, to determine the components of a noise figure matching circuit, with relative ease, using a network analyzer and a noise figure meter. If the antenna gain is known, then the radiated receiver sensitivity can be predicted. However, if the measured radiated sensitivity is worse than the prediction, then the difference can generally be attributed to microprocessor noise.

Once this effect is understood, engineers can address the effect of such noise rather than optimizing other circuit parameters. This can save a company valuable development time. In this article, we present two methods for characterizing antenna radiation performance in terms of dBi, or gain over an isotropic radiator. Once this is done, the radiated receiver sensitivity can be predicted and compared to the measured sensitivity.

First, the best noise figure (NF) matching circuit is found using the noise figure meter as shown in figure 1a. In general, determining the optimum impedance needed at the input of the low-noise amplifier (LNA) is done by adjusting the components of the matching circuit until a desired noise figure is achieved. Once this is attained, the LNA can be disconnected from the NF meter and the matching circuit can be examined on a network analyzer to ascertain Z_opt of figure 1b. The 50Ω impedance shown in figure 1b is the internal network analyzer impedance.

Next, the antenna is matched so that its impedance, Z_ant, is nearly equal to Z_opt. This is achieved by adjusting capacitors C₁, C₂, and C₃ (see figure 2, where a small loop antenna is used as an example).

A practical circuit that results in optimum LNA NF is an inductor in series with a capacitor, as shown in figure 3a. The resulting circuit at the LNA input is shown in figure 3b. From experience, the values shown in table 1 work quite well as optimum noise impedances.

The next task involves antenna measurement test facilities, such as an antenna range or anechoic chamber. Such facilities consists of a transmitting and receiving system as shown in figure 4, where a signal generator is used for transmitting signals, and a spectrum analyzer for receiving them. A two-port network analyzer can also be used.

A common method of characterizing antennas is the substitution method¹. First, the signal received by a calibrated 50Ω dipole antenna is recorded. Next, the dipole is replaced with the antenna under test. The difference of the two receiving signals (in dB) indicates how well the test antenna performs as compared to the dipole. For example, if the test antenna's received signal is 23 dB below that of the dipole, then the antenna gain is -23 dBd. To convert to dBi, subtract 2.2 dB (or -25.2 dBi). This is because the dipole antenna gain is 2.2 dB higher than an isotropic antenna.

The antenna substitution method involves only passive antennas (no active circuits). In this case, the method was modified by using active or powered antennas and the receiver. To test the dipole, the circuit of figure 3b was used. The 50Ω load was replaced by the 50Ω dipole antenna (figure 5a). Therefore, the LNA still “sees” the optimum impedance, Z_opt. For the loop antenna testing, the components of figure 2 were used at the LNA input, as shown in figure 5b. In both cases, the impedance at the input of the LNA is similar.

So, for this case, C, L, and dipole (see figure 5a) were substituted with C₁, C₂, C₃ and loop antenna (see figure 5b). Next, the receiver sensitivity was determined, for both cases, by modulating the carrier according to the system protocol. The difference in sensitivity levels is the gain of the receiver antenna as compared to that of the dipole, or the gain in dBd. Adding an additional 2.2 dB will result in the antenna gain in dBi. It should be noted that the antennas and LNA of figure 5 should be physically separated (normally a few inches) from the receiver so that the microprocessor noise does not affect the measurement.

Using a different technique, it is possible to determine the antenna gain based on measurements of injected sensitivity, transverse electromagnetic (TEM) cell radiated sensitivity, receiver input impedance, and antenna impedance. The advantage of this technique over the substitution method is that no antenna range or anechoic chamber is needed to find the antenna gain. The diagram shown in figure 6 presents a receiver with the antenna, matching network, and referenced impedances. Note that the matching network is adjusted such that the LNA “sees” Z_Opt when the antenna is connected.

When an injected sensitivity measurement is performed, typically, the receiver antenna is disconnected at point A in figure 6 and a signal generator is connected in its place. The circuit in figure 7 models the injected sensitivity measurement, where the signal generator is modeled as a source, V_s, with impedance Z_s (in this case 50Ω), and the receiver is modeled as a load having impedance Z_L.

The first step in this procedure is to disconnect the antenna at point A into which the injected receiver sensitivity source power available (P_AVS), is measured using a 50Ω signal generator by modulating the carrier according to the system protocol.

Next, we measure the magnitude of the reflection coefficient, |S₁₁|, at point A of the receiver with a 50Ω network analyzer. The actual injected power, P_LI, delivered to the receiver is²:

P_LI = P_AVS (1 -|S₁₁|²) (1)

Where: P_AVS is the power available from the generator (the calibrated signal generator reading corresponding to the receiver sensitivity). P_LI is the actual power delivered to the receiver. The rest of the available power is reflected back towards the signal generator.

The next step will consider the radiated case. The antenna is reconnected at point A to the matching network such that the LNA sees Z_opt (see figure 6). The receiver in located in a TEM cell in a “best position” (best position refers to the antenna orientation resulting in maximum gain) and the radiated sensitivity is measured. The circuit in figure 8 models the system with the antenna connected to the receiver. The antenna is modeled as a source V_A with impedance Z_A, while Z_L is the same impedance as shown in figure 6.

A similar equation to that of the injected case² is then written:

P_LR = P_AVA (1 -Γ|²), (2)

Where P_AVA is the power available from the antenna, and Γ is the reflection coefficient between the antenna and receiver at point A in figure 6. P_LR in this case is the power delivered from the antenna to the receiver. To calculate Γ, we must measure Z_A and use the following equation²:

For the purpose of this procedure, we postulate that, at sensitivity, the following equation holds:

P_LI = δP_LR, (4)

where P_LI is the receiver sensitivity and δ is a correction factor. When the antenna is replaced with a 50Ω signal generator to measure sensitivity, the system NF will increase. This is due to presenting the LNA with impedance other than Z_opt. The factor δ accounts mainly for the decrease in sensitivity resulting from the increased system NF.

Equation 4 indicates that regardless of whether an antenna or a signal generator is connected at the receiver input, the receiver will respond to the same delivered power level multiplied by a correction factor.

The correction factor can be found by using the setup in figure 9 to measure NF₂. The matching network should be the same one used to transform the antenna impedance Z_A to Z_opt. Once the new noise figure NF₂ is measured, δ can be computed by:

Where NF₁ is the optimum NF corresponding to Z_opt, and NF₂ is the noise figure corresponding to source impedance resulting from replacing the antenna with 50Ω. Since we calculated P_LI from equation 1, P_LR can be calculated from equation 4. Next, we can calculate P_AVA using equation 2, which is the power available from the antenna corresponding to the radiated sensitivity power level. This quantity will help us find the gain as discussed below.

The radiated sensitivity measurement is obtained from the signal generator reading connected to the TEM cell (usually in dBm). Next, the power corresponding to the radiated sensitivity of the receiver (Pr) must be converted from dBm to volts per meter (V/m) using the TEM cell equation 6⁴. This quantity is represented as E_r:

where d is the TEM cell distance (in meters) between the septum and the top or bottom. From antenna theory, it can be shown that³:

where E_r is the measured sensitivity in V/m, f is the operating frequency in Hz, and G is the antenna gain. Substituting for P_AVA and performing a simple manipulation, yields the antenna gain, G:

The following example illustrates this procedure. A super-regenerative receiver that employs a PCB trace as its antenna is used with the following measurement results obtained at f = 315 MHz: Injected 50Ω sensitivity; P_AVS = 1.0 × 10^-13 W, TEM cell sensitivity; (E_r) = 288.4 × 10^-6 V/m, antenna impedance; Z_A = 19 - j41 W, input impedance: Z_L = 4.3 + j67 W, |S₁₁| of input = 0.94. Using equation 3, G = 0.274 + j0.811, which gives |G| = 0.86. In this case, P_LR = P_LI. Finally, substituting for all the values in equation 8 gives the antenna gain = -25.6 dBi.

Next the parameters that may affect the accuracy of this method are discussed. It is assumed that there is no loss of sensitivity due to module noise pickup by antenna. This can introduce a significant error if the receiver has a noisy microprocessor. In this case, it is possible to reduce this uncertainty if the antenna is moved away from the receiver to reduce this effect. Ohmic losses in the antenna are ignored in equation 6. A tiny portion of the incoming signal is bypassing the antenna and entering the receiver directly. This effect can also be ignored in many cases. Finally, equation 6 is only valid in the far field.

This article has described two methods for determining the antenna gain of miniature receivers. Even though more labor intensive, the substitution method provides extremely accurate information on antenna gain. The alternate method provides less, but still relatively accurate results. Both methods can reduce the development time of miniature receivers by giving the designer accurate information on antenna gain.

1. C. Balanis,C. Antenna Theory. New York: John Wiley & Sons Inc., 1982.

2. Gonzalez, G. Microwave Transistor Amplifiers. 2d ed. New Jersey: Prentice Hall, 1997.

3. Vizmuller, P., RF Design Guide. Massachusetts: Artech House, 1995.

4. Crawford, M., “Generation of Standard EM Fields Using TEM Transmission Cells.” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-16, No. 4, 1974, pp. 189-195.

Riad Ghabra is currently a senior RF engineer with Lear Corp. (www.lear.com). He has worked on automotive related RF products since 1998. Prior to that, he worked for Motorola Inc. (www.motorola.com) Paging on RF receivers. He received his B.S.E.E. and M.S.E.E. from Virginia Tech in 1989 and 1991, respectively. He is a co-inventor of several automotive related patents. He may be reached at ghabra@yahoo.com.

Argy Petros (formerly Argyrios Chatzipetros) received his M.S. and Ph.D. degrees in electrical engineering from Virginia Tech in 1990 and 1994, respectively. From May 1993 to November 1998 he was with Motorola Inc. working in the development of several wireless products. From December 1998 to April 2003, he was with XM Satellite Radio Inc. (www.xmradio.com). He's currently a consultant at Think Wireless Inc. (www.thinkwireless.com). In 2002 he was inducted into NASA's Space Technology Hall of Fame. He holds 12 U.S. patents and is a senior member of the IEEE (www.ieee.org). He may be contacted at argy@thinkwireless.com.