# Engineering rules and design charts.

ENGINEERING RULES AND DESIGN CHARTS

In this section, a collection of tables, charts and nomographs of EW engineering data is presented. The material has been gathered from a variety of sources including the personal collections of the users of this Handbook. The editor acknowledges with thanks these inputs.

RULES OF THUMB

This series of radar and antenna formulas includes fundamental radar relations as well as a concise tabulation of antenna gain and beamwidth properties. The material is reprinted from Radar Evaluation Handbook, edited by D.K. Barton, C.C. Cook and P. Hamilton, editors, and published by Artech House, Norwood, MA, 1991.

Rules of Thumb Frequency and Wavelength [Mathematical Expressions Omitted] Average Power [Mathematical Expressions Omitted] Unambiguous Range [Mathematical Expressions Omitted] Solid Antenna Beam Angle [Mathematical Expressions Omitted] Observation Time (Time-on-Target) [Mathematical Expressions Omitted] Horizon Range [Mathematical Expressions Omitted] Doppler Frequency [Mathematical Expressions Omitted] Angle Accuracy (Thermal Noise) Sector Scanning [Mathematical Expressions Omitted] Monopulse Tracking [Mathematical Expressions Omitted]

SENSITIVITY AND THE RECEIVED PULSE DENSITY

Once a threshold power level is established for a receiving system, we assume that signal pulses which exceed this level are processed by the receiver. For a given emitter and receiver, we can compute the maximum range at which that emitter can be received. In the case of an airborne receiver, however, if the maximum range is less than the altitude at which the aircraft is flying, no signals will be received. As the altitude decreases, a region is defined on the earth's surface in which all emitters of that type can be received. As the altitude continues to decrease, at some point, the distance to the horizon will be less than the maximum range at which the emitter can be received and the number of pulses begins to decrease.

The figure gives the altitude at which the maximum number of pulses may be received as a function of the receiver sensitivity, assuming a wavelength of 10 cm and transmitter losses equal to ELINT receiver losses. Thus, to fly at 10,000 m and receive sidelobe signals from a 1-kW transmitter at the horizon requires a sensitivity of -83 dBm. This curve was reprinted from R.G. Wiley, Electronic Intelligence: The Interception of Radar Signals, Artech House, Norwood, MA, 1985.

ESM FUNDAMENTALS

This collection of electronic support measures (ESM) equations provides an insight into the relationship of sensitivity and detection range. The final series of expressions deals with signal processor gains. This material was prepared by Don Margerum, Raytheon Co., Electromagnetic Systems Division, Goleta, CA.

ERP RELATIONSHIP OF ON-BOARDS AND OFF-BOARD JAMMERS

This unusual nomograph allows the design engineer to predict the ratio of effective radiated power (ERP) of an on-board jammer to a decoy jammer. The material was prepared by Lee Meadows, Raytheon Co., Electromagnetic Systems Division, Goleta, CA, and is an addition to a nomograph contained within "Stairsteps to ERP" by Simon W. Barnhart which originally appeared on p. 72 of the September 1979 issue of Microwave System News.

This chart provides a rapid method for generating ballpark estimates of jammer ERP requirements for both on-and off-board systems. The variables are divided into 10-dB increments and are arranged in a connecting staircase. This presentation provides a rapid and visual method of computation. All definitions and units may be found in the figure.

As useful as this nomograph is, more precise solutions to ECM equations may be generated by use of a computer program entitled "[E.sup.3]: ECM Equations by E-Systems." Copies of this IBM compatable software, which solves eight frequently used radar jamming equations, may be obtained at no cost by contacting Ms. Pat Stafford, Coordinator of Strategic Development, E-Systems, Inc., Melpar Division, 7700 Arlington Blvd., Falls Church, VA 22046, (703) 849-1625.

This nomograph provides a solution to the equation:

S = ([P.sub.rG.sub.rI.sup.2])/[(4[pi]).sup.2R.sup.2] where:

S = the incident energy density in dBm

[P.sub.r] = the radar output power

[G.sub.r] = the antenna gain

I = the wavelength

r = the range in nautical miles.

Thus, for an output of 10 kW at 1 GHz and a gain of 40 dB, S at 50 nmi is -22 dBm. This nomograph was supplied by Richard Udd, Raytheon Co., Electromagnetic Systems Division, Goleta, CA.

ANTENNA PROPERTIES

Three design charts present (1) free-space propagation loss as a function of frequency and distance; (2) the aperture gain of an antenna from 1.0 to 40 GHz; and (3) the directive gain of an antenna with various combinations of azimuth and elevation beamwidth. These charts were prepared by Dave Thomas of Raytheon Co., Electromagnetic Systems Division, Goleta, CA.

RANGE AND DEPRESSION ANGLE RELATIONSHIPS

This figure relates the optical range in nautical miles from a platform at altitudes varying from 1,000 to 60,000 ft over the earth as a function of depression angle. This set of curves was supplied by Richard Udd, Raytheon Co., Electromagnetic Systems Division, Goleta, CA.

PHOTO : OPTIMUM ALTITUDE AS A FUNCTION OF RECEIVER SENSITIVITY

PHOTO : ESM SENSITIVITY & DETECTION RANGE CALCULATION

PHOTO : ESM SENSITIVITY CALCULATION

PHOTO : EMPIRICAL EXPRESSIONS FOR SIGNAL PROCESSING GAIN

PHOTO : ESM DETECTION RANGE CALCULATION

PHOTO : FREE-SPACE PROPAGATION LOSS (dB) = 10 LOG([lambda]/4[pi]R)[.sup.2]

PHOTO : NOMOGRAPH FOR A SOLUTION OF ONE-WAY RADAR RANGE EQUATION

PHOTO : DIRECTIVE GAIN, G1, AS A FUNCTION OF BEAMWIDTH

PHOTO : GAIN OF APERTURE ANTENNA (50% EFFICIENCY)

PHOTO : RANGE VERSUS DEPRESSION ANGLE AS A FUNCTION OF ALTITUDE
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