Radar systems work by detecting signals reflected by a target. If the radar cross section (RCS) of the target can be made to look smaller, a target can often be hidden or disguised from a radar. This of course is the key concept which enables “stealth” technology for military aviation. During active operations, damage to the aircraft can result in an undesirable increase in RCS, exposing the aircraft to the adversary’s radar. Repair of the aircraft can often be accomplished on the flight line, but confirmation that the repair has not compromised the aircraft’s RCS (which could lead to undesired detection by the adversary) has previously required that the aircraft be taken out of operation and transported to a test facility. Today the RCS of an aircraft can be easily determined on the flight line utilizing the MS2038C VNA Master™, a portable vector network analyzer from Anritsu Co.

RCS measurements determine the capability of a target to reflect a radar signal in the direction of a radar receiver. They are a measure of the ratio of signal backscatter per steradian (unit solid angle) in the direction of the radar (from the target) to the power density that is intercepted by the target. A target’s RCS can be visualized (Fig. 1) as a comparison between the power reflected by the target and the power reflected by a reference, a perfectly conducting smooth sphere with RCS area of one square meter (1 m2). The RCS of a sphere is independent of frequency provided that the wavelength, λ, is much less than the range, R, to the target (such as R > 15λ) and the effective radius of the target, rt, such that r t > 15λ.

The radar system described in Fig. 2 transmits a pulse of energy through the transmit antenna which exhibits a gain of Gt. The amplitude of the signal at the output of the transmit antenna is reduced by the free-space propagation loss. At the target, some of the power (backscatter) is reflected back towards the radar. The ratio of the backscatter power to the incident power is the RCS (ótarget) for the target. The amplitude of the signal is then again further reduced by the free-space propagation loss. The signal is then received by the receive antenna with gain of Gr and detected in the receiver. The power level, Pr, in the radar receiver can be found from:

Pr = [PtGtGrótargetλ2]/[(4ð) 3R4] (1)

where:

Pt = the power level in the radar transmitter;
Gt = the gain of the radar transmitter antenna;
Gr = the gain of the radar receiver antenna;
ótarget = the RCS of the target (in m2);
λ = the wavelength of the radar signal (in m); and
R = the range from the transmitter/receiver to the target (in m).

Most radars operate in a monostatic configuration, using a common transmit and receive antenna and a duplexer to separate transmit and receive signals. Figure 3 shows a physical representation of a radar, using the parameters presented in Eq. 1. Additional terms in this block diagram (beyond Eq. 1) include:

G0 = the equivalent gain of the RCS and
Ac = the effective area of the radar receive antenna (in m2).

It should also be noted that ótarget, the RCS of the target, is essentially the ratio of the received radar power to the transmitted radar power, or kPr/Pt, where k is a proportionality constant.

The RCS for any target, ótarget, can be found from:

ótarget = (Pr[(4ð)3R4/(GtGrλ2)]/Pt) = k(Pr/Pt) (2)

An equivalent-circuit description of a radar system is shown in Fig. 4. Transmit and receive antenna gains are represented by amplifiers. Resistors are used to represent propagation losses. When a VNA is used to measure the forward transmission, S21, of a device, it has the same equivalent-circuit description as a radar. The VNA measures the frequency-domain response of the system when the analyzer’s port 1 is connected to the transmit antenna and port 2 is connected to the receive antenna (Fig. 5).

The time-domain function built into the MS2038C portable VNA simulates the radar and accurately measures the RCS of the target. The VNA’s 12-term error-correction algorithm helps minimize systematic errors due to impedance mismatches and signal leakage, while its time-domain functionality (which simulates a pulsed radar) is used to remove most of the spurious reflections that can degrade RCS measurement accuracy.

In making RCS measurements with a VNA, it is important to realize that the polarization of the reflected signal’s electric field vector can be different than that of the transmitted signal. The shape of the target will impact the depolarizing characteristics (the angular difference of ãt – ãr) as depicted in Fig. 2.

To correct for depolarization, full polarization matrix imaging is used by measuring both the vertical and horizontal components of the electric-field independently. This requires two transmit and two receive polarizations [transmit and receive horizontal (H) and vertical (V) polarizations]. When signals with vertical polarization are transmitted, the receiver measures both vertical and horizontal polarization. When signals with horizontal polarization are transmitted, the receiver also measures vertical and horizontal polarization. With these results, a polarization matrix can be generated by the two parts of Eq. 3 to describe the effect of the polarization and correct for depolarization:

Et = Etv cos(ãt + Ethsin(ãt)
Er = Erv cos(ãr + Erhsin(ãr) (3)

Parameters Et and Er can be decomposed to the two parts of Eq. 4:

Erv = SvvEtv + ShvEth
Erh = SvhEtv + ShhEth (4)

where Sxx = a complex number defining the four possible measurement conditions:

where:

Svv= transmit vertical polarization with receive vertical polarization;
Svh = transmit vertical polarization with receive horizontal polarization;
Shv = transmit horizontal polarization with receive vertical polarization; and
Shh= transmit horizontal polarization with receive horizontal polarization.

The resulting RCS is:

If the transmit antenna is vertically polarized, the RCS is:

ù = (Prv + Prh)/Pt (7)

A VNA measures scattering (S) parameters in the frequency domain. The frequency range is selected for a band of interest, such as 8.2 to 12.4 GHz for WR-90 X-band waveguide. The VNA’s time-domain function transforms the S-parameter data from the frequency domain à versus frequency) to the time domain (à versus time or distance).

Due to a phenomenon known as the alias free range, which is related to the transformation of signal information from the frequency to the time domain, a target should not be placed greater than a certain distance from the VNA. The transform process in a VNA is a circular function that repeats itself periodically outside its inherent time range of t = 1/(frequency step size). The frequency step size is proportional to the frequency span and inversely proportional to the number of data points, or:

Inherent time range: t = (N – 1)/(frequency span)

For example, at X-band, using a 4-GHz frequency span and 4001 data points, the alias free range (AFR) is 4000/4 GHz = 1000 ns, corresponding to a 300-m AFR. The 300-m range is the round-trip time. Thus, to avoid alias ambiguities, the target should not be placed more than 150 m from the VNA. The maximum power output of the standard MS2038C (at 4 GHz) is −3 dBm. The noise floor of the VNA with a 25-dB-gain low-noise preamp is approximately −115 dBm at a 10 Hz IF bandwidth. The round trip loss for a 50-m range to the target is 112 dB. The signal level for a target with a radar cross section of ó = 0.1 m2 and a port power of +10 dBm is approximately −102 dBm which yields the signal-to-noise ratio of 10 dB required for accurate measurements. This requires an auxiliary power amplifier with a least +10 dBm output power.

If the RCS of the target is >1 m2 then no power amplifier is required.

Figure 5 shows a simple block diagram for a typical RCS measurement configuration using a VNA. The transmit antenna (which is connected to port 1 of the VNA) and receive antenna (which is connected to port 2 of the VNA) are positioned in the same plane, as shown in the block diagram. The object to be measured consists of a target either mounted in a pedestal or a stand-alone aircraft on a flight line.

Performing an S21 measurement with a VNA is very much the equivalent of the way in which a radar operates. The coaxial cable output for the VNA’s port 1 is connected to the coaxial-to-rectangular-waveguide transition (with the E field in the vertical direction). The output of port 2 is connected to the output of the receive waveguide antenna. Both antennae are located as close together as possible, in either a vertical or horizontal plane. To develop the polarization matrix, both transmit and receive antennae should be capable of 90-deg. rotation. The target should be located at a distance less than AFR/2 but far enough from the antenna to insure that the entire target will be illuminated by the antenna beams.

A full 12-term calibration is performed at the output of the coaxial cables to establish the reference plane for the RCS measurement. An S21 frequency-domain measurement is performed on the target. The S21 data is transformed to the time domain using bandpass processing. Figure 6 presents the screen of a portable VNA where all reflections are shown. The target reflection is identified and a range gate is placed on the target to remove all other reflections from the data, with Fig. 7 showing the results of this signal subtraction. The magnitude of the S21 time-domain amplitude of the target reflection is then measured.

To calibrate the RCS measurement setup, the target is replaced by an RCS standard. Examples of RCS standards of known geometries and their corresponding cross sections are shown in Fig. 8. The ideal calibration standard is a conducting sphere of known diameter. A 1.13-m diameter sphere has an RCS of 1 m2, independent of frequency. The diameter of the calibration sphere can be chosen for an RCS corresponding as closely as possible to the expected RCS of the target to be measured, although any geometry can be used for the sake of performing a calibration.

An S21 frequency-domain measurement is performed on the calibration standard to be measured. The S-parameter data is transformed to the time domain mode using bandpass processing and an appropriate time gate is placed on the standard’s location. The magnitude of the time-domain S21 amplitude for the reflections from the standard are then measured. This measured value is the reference for the RCS measurement. Using a sphere with an RCS of 1 m2 as the calibration standard, then the RCS of the target is:

RCStarget(dBsm) =

RCSstandard measurement(dB) − RCStarget measured(dB)

RCS data calculated by this equality are expressed in decibels referenced to one square meter (dBsm). An RCS value in square meters can be converted to dBsm by using the relationship:

dBsm = 10log(RCS m2)

Using a portable VNA to make RCS measurements offers a convenient and flexible solution for data gathering once associated with large and expensive rack-mount systems. A portable instrument such as the VNA Master can be easily transported to a site where testing is needed, and measurements made easily by following a simple, step-by-step procedure:

  1. Set up the antenna bracket for the S11 and the S21 antennas.
  2. Attach the S11 (with vertical polarization), the S21 (with vertical polarization), and the S21 (with horizontal polarization) antennas to the portable analyzer.
  3. Connect port 1 of the analyzer to the S11 antenna and a coaxial cable assembly from port 2 of the analyzer to the corresponding S21 vertically polarized and S21 horizontally polarized waveguide horn antennas.
  4. Perform a 12-term calibration, such as an open-short-load-thru (OSLT) or line-reflect-match (LRM) calibration, at the output cables from port 1 and port 2 of the portable VNA.
  5. Perform the isolation term calibration by using a large slab of absorber material at the output of the waveguide horns.
  6. Measure the calibration standard at the location specified (d > 20ë and within −1-dB azimuth and elevation angles of the antenna) and plot both S11 and S21 in the time domain with a range gate applied to the target. The RCS of the calibration standard should be slightly greater than the estimated RCS of the target.
  7. Replace the calibration standard with the target and repeat the measurements of Step 6.
  8. If a support structure is used for the target, measure the S11 and S21 values of that support structure. This value should be −20 dB below that of the target calculated RCS (S11 of the support structure << S11 of the target). If this is not the case, add microwave absorber material around the support structure to reduce its RCS to an acceptable value.
  9. The signal level of the calibration standard is translated to an RCS reference in dB for an RCS of 1 m2.
  10. The RCS of the target is then calculated using the following derivation from the classic radar range equations:

If a support structure is used for supporting the calibration standard then the S21 of the structure should be less than S21/10 of the target or the standard for accurate measurement. It may be necessary to cover the support structure with radar absorbing material:

PR = (PTGTGR2óDUT)/[(4ð)3R4]
Pstd = (PTGTGRë2óstd)/[(4ð)3R4]
Ptgt = (PTGTGRë2ótgt)/[(4ð)3R4]
Pstr = (PTGTGRë2óstr)/[(4ð)3R4]

where:

Pstd refers to the reflected power from the RCS calibration standard, Pgt refers to the reflected power from the target, and
Pstr refers to the reflected power from the support structure.

The forward transmission losses, S21, for the calibration standard, RCS target, and antenna support structure can be found from these three equations:

S21 std = 10log(Pstd/PT)
S21tgt = 10log(Ptgt/PT)
S21str = 10log(Pstr/PT)
Pstd/PT = 10exp[S21 std/10]
Ptgt/PT = 10exp[S21 tgt/10]
Pstr/PT = 10exp[S21 str/10]

The return losses, S11, for the calibration standard, the RCS target, and the antenna support structure can be found by applying the following two sets of three equations:

S11std = 10log(Pstd/PT)
S11tgt = 10log(Ptgt/PT)
S11str = 10log(Pstr/PT)
Pstd/PT = 10exp[S11 std/10]
Ptgt/PT = 10exp[S11 tgt/10]
Pstr/PT = 10exp[S11 str/10]

and then the following equations can be applied to calculate the target’s RCS:

Ptgt/Pstd = ótgtstd
= 10exp(S11 tgt - S11 std)/10]
ótgt = óstd10exp[(S11 tgt - S11 std)/10]

As has been shown, the MS2038C VNA Master from Anritsu Co. can be used in the field to provide quite serviceable RCS measurements on a wide range of targets. This particular model operates from 5 kHz to 20 GHz with measurement speed of 350 µs per data point and includes a spectrum analyzer with frequency range from 9 kHz to 20 GHz. It offers a fully reversing two-port, two-path measurement system and incorporates the 12-term error-correction algorithm essential for calibrating the analyzer to remove the effects of spurious reflections.