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The beam solid angle of an antenna is the integral of its normalized radiated-power pattern over the complete sphere. If $U(\theta ,\varphi )$ is radiated power per unit solid angle and $U_{\max }$ is its maximum, thenIt is measured in steradians and includes sidelobes and backlobes, not just a chosen main-beam boundary. Since total radiated power is $P_{\mathrm{rad}}=\int Ud\Omega$, peak antenna directivity satisfiesThe definition relates concentration of radiation to the entire pattern, rather than to a single width measurement.^[ref]

For a narrow, axisymmetric Gaussian power pattern $U/U_{\max }=e^{-{\theta }^2/(2{\sigma }^2)}$, replace $\sin \theta$ by $\theta$ near the axis and extend the negligible tail to infinity. The resulting Gaussian beam solid angle is ${\Omega }_A\simeq 2\pi {\sigma }^2$. Its full half-power width is ${\theta }_{\mathrm{HP}}=2\sqrt{2\ln 2}\sigma$, so ${\Omega }_A\simeq \pi {\theta }_{\mathrm{HP}}^2/(4\ln 2)$. These approximations require a narrow beam with no significant additional lobes; a broad pattern or strong sidelobes requires the full integral.

C. W. Wang is credited by that name as coauthor with T. Keech of Antenna Models for Electromagnetic Compatibility Analyses by C. W. Wang and T. Keech. The primary title page identifies the authors and the October 2012 memorandum; it does not justify guessing a full personal name or using a portrait of another Wang.^[ref]

The report compiles radio-antenna radiation patterns, gain values and sidelobe requirements for electromagnetic compatibility studies. These inputs determine how strongly a transmitter radiates toward an unintended receiver, so using a realistic pattern can change an interference calculation even when total transmitted power is unchanged.^[ref]

Electromagnetic compatibility is the ability of electrical equipment to operate as intended in its electromagnetic environment without causing unacceptable disturbance to other equipment. Emission and immunity are complementary questions: how strongly does a device disturb its surroundings, and how well does it tolerate disturbances arriving from them?

Interference requires a source, a coupling path and a susceptible receiver. A switching power converter may couple a disturbance into a sensor through shared supply impedance, capacitive coupling or radiated fields. In an illustrative circuit, a $0.2$ A switching-current change through a shared $0.1\Omega$ return impedance produces a $20$ mV reference shift, potentially much larger than the sensor signal. A balanced connection and finite common-mode rejection ratio help only to the extent that the disturbance remains common to the two inputs.

A useful test compares the sensor output with the converter switched on and off, then deliberately changes the coupling path or applies a calibrated disturbance. Antenna patterns, cable routing, grounding and frequency all enter the inference; passing one test configuration does not imply immunity to every disturbance.^[ref]

For a narrow axisymmetric Gaussian power pattern $P(\theta )/P(0)=e^{-{\theta }^2/(2{\sigma }^2)}$, the beam solid angle is approximatelyThe approximation replaces $\sin \theta$ by $\theta$ and extends a negligible angular tail. If $\Theta$ is the full half-power beamwidth, then $\Theta =2\sqrt{2\log 2}\sigma$ and ${\Omega }_A\simeq \pi {\Theta }^2/(4\log 2)\approx 1.133{\Theta }^2$, with angles in radians. This is a power-pattern convention; a Gaussian field-amplitude width uses a different factor.

For $\Theta =0.1$ radians the solid angle is approximately $0.01133$ steradians, giving peak antenna directivity $4\pi /{\Omega }_A\approx 1109$. Rotating a calibrated source or receiver and measuring the whole angular pattern tests the approximation: significant sidelobes contribute extra solid angle that a main-beam width cannot detect.^[ref]

T. Keech is credited, under that initial and surname, as coauthor with C. W. Wang of Antenna Models for Electromagnetic Compatibility Analyses by C. W. Wang and T. Keech, an October 2012 NTIA technical memorandum. The title page verifies this attribution but is not a basis for expanding the initial or choosing a portrait of a namesake.^[ref]

The report assembles antenna gains, radiation patterns and sidelobe parameters for assessing interference between radio systems. Its scientific role is to make the assumed angular concentration of radiation explicit when comparing unwanted received power between systems.^[ref]