Est Formulas

1 | E S T F o r m u l a s

Compiled by: MIT - TEAM4A [Santos, Moreno, Mallari, Malana, Lineses, Jimenez, Garcia, Gamboa, Dahilog, Baduria]

BASIC COMMUNICATIONS

Wavelength

=

Frequency

= 1

Bandwidth

=

Resonant Frequency

= 12 Varactors Capacitance

= 1 + 2

Crystal Thickness

= 65.5

Oscillator Operating Frequency @ Certain Temperature

= + ( ) Audio Power

= 0.5 Audio Power

= 22

Audio Power

= 0.5 Amplifier Efficiency

=

Load Impedance

= Load Resistance

= 22 Collector Voltage

( ) = 4 Quality Factor

=

Shape Factor

= 606

Image Frequency

= + 2 Image Frequency Rejection Ratio

=



Image Frequency Rejection Ratio

= 1 + 22 =

VCO Sensitivity

= Coupling Coefficient

= 1

Optimum Coupling Coefficient

= 1.5 Bandwidth

=

MODULATION

Modulation Index

=

= +

Total Modulation Index (AM)

= 12 + 22 + + 2 Upper and Lower Sideband Voltage

= = 2

Upper and Lower Sideband Frequency

= = +

Bandwidth (AM)

= 2 Total Transmitting Power

= 1 + 22 Total Sideband Power

= 22 Power Saving of Double Sideband Suppressed Carrier

%. . =

100 Peak Envelope Power

= 22 Emitter Modulator Voltage Gain

= (1 ) Modulation Index for Single Sideband

= 2

Quality Factor

= (1/20 )4



FM Modulator Sensitivity

= Deviation Ratio

= ( ) Percent Modulation (FM)

% =

100 Carrier Swing

. . = 2 FM Bandwidth Carsons Rule

= 2 + (max ) FM Exact Bandwidth

= 2 FM Narrow Bandwidth

= 2 FM Wideband Bandwidth

= 2 Noise Phase Shift

= 1 ;

PM Modulator Sensitivity

=

NOISE

Effective Noise Bandwidth

= 2 Total Harmonic Distortion

% =

100 Noise Power

= Noise Voltage

= 12 + 22 + 32 + + 2 Shot Noise

= 2 Signal-to-Noise Ratio

/() = 10log(/) Signal-to-Noise Ratio

/() = 20log(/) Noise Factor

= (/)(/) Noise Figure

() = (/) (/) Total Noise Factor

= 1 + 2 11 + 3 112 + 4 1123



Equivalent Noise Temperature

= 290( 1)

RADIO WAVE PROPAGATION

Velocity of Propagation

=

Characteristic Impedance

=

Relative Permittivity

= Characteristic Impedance of a Medium

= 377

Power Density

= 2 Power Density

= Power Density

= 42 Effective Isotropic Radiated Power

=

Power Density

= 42 Electric Field Intensity

= 30

Effective Antenna Area

= Received Power

= 42 Effective Antenna Area

= 24 Snells Law

11 = 22 Refractive Index

= Snells Law

12 = 12

Critical Angle

= 1 21



Maximum Usable Frequency

= 1

Optimum Working Frequency

= 0.85 Distance between Transmitting and Receiving Antennas

= 17 + 17 Distance between Transmitting and Receiving Antennas

= 2 + 2 Free Space Loss

= 32.4 + 20 + 20 Time between Fades

= 2 Number of Cells

= 3.4642

ANTENNAS

Radial Length

= 142.5

Radiation Resistance

= 2

Antenna Efficiency

=

; = +

Dipole Gain

() = () 2.14 Antenna Power Gain

= Effective Isotropic Radiated Power

= Folded-Dipole Impedance

= 732 Helical Antenna Gain

= 15()23

Helical Antenna Beamwidth

= 52

Parabolic Antenna Beamwidth

= 222

Passive Reflector Gain

= 2042 Parabola Coupling Factor

= 4



TRANSMISSION LINES

Wavelength

=

Velocity Factor

= 1

= Velocity of Propagation

=

Propagation Time

=

Characteristic Impedance

= Characteristic Impedance of Parallel-Wire Cable

= 276

log

Characteristic Impedance of Balanced 4-wire

= 138

10 22 1 + 212

Characteristic Impedance of Balanced wire near Ground

= 276

10 2 1 + 22 Characteristic Impedance of Wires in Parallel near Ground

= 69

10 4 1 + 2 2 Characteristic Impedance of Balanced 2-wire near Ground

= 276

10 2 1 + 2412 Characteristic Impedance of Coaxial Cable

= 138

Reflection Coefficient

= +

Reflection Coefficient

= 1 + 1

Phase Shift

= (360)

Standing Wave Ratio

=



Standing Wave Ratio

= 1 + ||1 || Standing Wave Ratio

=

=

Standing Wave Ratio

= 1 + /1 / Load Power

= 4(1 + )2 Reflected Power

= 2 Load Power

= (1 2) Impedance Matching

12 = 122

Quarter-wavelength Transformer Characteristic Impedance

= Microstrip Characteristic Impedance

= 87 + 1.41 ln 5.980.8 +

Stripline Characteristic Impedence

= 60

ln 40.67 0.8 + Open-Wire (Microstrip) Transmission Line

= 120 ln +

FIBER OPTICS

Index of Refraction

=

= Snells Law

11 = 22 Critical Angle

= 1 21 Numerical Aperture

= 12 22 =

Maximum Acceptance Angle

= 1(12 22) Acceptance Cone

= 2



Single Mode Cutoff Wavelength

= 2122.405 Maximum Radius

= 0.383 Number of Modes

= 22 Bandwidth

= 12 Electrical Bandwidth

= 0.35

Fiber Attenuation

= 10/10 Photon Energy

= Total Rise Time

= 2 + 22 Bit Rate for UPRZ Code

= 1 Bit Rate for UPNRZ code

= 12

Bit Rate for NRZ Code

= 1 Bit Rate for RZ Code

= 12 Bandwidth-Distance Product

= 500

Responsivity

=

Responsivity

= 1234 Irradiance

=



TELEPHONY

Pulse Dialing Duration

= (0.1) + ( 1) Tone Dialing Duration

= + ( 1) DC Loop Resistance

= 0.10952 Grade of Service

=

Traffic Intensity

= Carried Traffic

= (1 ) Trunk Utilization

=

Via Net Loss

= 0.2 + 0.4() Crosstalk Decibel Unit

= 90 Number of Full-Duplex Cellular Channels

=

Total Channel Capacity in a Cellular Area

= Frequency Reuse Factor

=

Co-Channel Reuse Ratio

=

Co-Channel Reuse Ratio

= 3 AMPS Transmit Carrier Frequency

= 0.03 + 825 = 0.03( 1023) + 825

AMPS Receive Carrier Frequency

= + 45 GSM Frequency Shift between Mark and Space

= 0.5 GSM Maximum Transmitted Frequency

= + 0.25 GSM Minimum Transmitted Frequency

= 0.25 CDMA Radiated Power

= 76



MICROWAVE DEVICES

Waveguide Longer Dimension

= 2 Rectangular Waveguide Cutoff Frequency

= 2 Rectangular Waveguide Cutoff Wavelength

= 2 Circular Waveguide Cutoff Wavelength

= 2 Group Velocity

= 1 22 Group Velocity

= 1 2 Phase Velocity

= 1 22

Phase Velocity

= 1 2

Group and Phase Velocity

= 2 Waveguide Characteristic Impedance

= 3771 2

Guide Wavelength

= Guide Wavelength

= 1 2

Magnetron Average Power

= Magnetron Duty Cycle

=

Horn Antenna Gain

= 7.52



H-Plane Beamwidth

= 70 E-Plane Beamwidth

= 56 Radar Equation

= 22(4)34 Radar Distance

= 2 Maximum Unambiguous Range

= 2 = 2

Minimum Usable Frequency

= 2 Doppler Shift Frequency

= 2

TERRESTRIAL MICROWAVE

Distance between Transmitter and Receiver

( ) = 2( ) + 2( ) ( ) = 17( ) + 17( )

K-Factor

= 11 0.046650.005577

Effective Earth Radius

= Earth Curvature

= 1( )2( )1.5 = 1( )2( )12.75

Fresnel Zone

= 17.3 1( )2( )( )1( )2( ) = 72.1 1( )2( )( )1( )2( )

Fresnel Zone Clearance

= 0.61



Fresnel Zone Clearance

= 43.3 1( )2( )( )1( )2( )

= 10.4 1( )2( )( )1( )2( )

Nth Fresnel Zone Radius

= 1 Effective Isotropic Radiated Power (EIRP)

= ( ) + () =

Free Space Loss

= 32.4 + 20( ) + 20( ) = 92.4 + 20( ) + 20( ) = 36.6 + 20( ) + 20( ) = 96.6 + 20( ) + 20( )

Isotropic Radiated Power (IRL)

( ) = Ratio of the Received to Transmitted Power

() = ( ) + ( ) () Availability

= +

Unavailability

= +

Reliability

= (1 ) 100 Antenna and Feedline Equivalent Noise Temperature

= ( 1)290 + Equivalent Noise Temperature

= 290( 1) Energy per Bit per Noise Density Ratio

= Noise Power Density

= Carrier-to-Noise Ratio

() = ( )

Receive Signal Level (RSL)

( ) = ( ) + () + () ()

Fade Margin

= 30 + 10 log(6 ) 10 log(1 ) 70



DIGITAL AND DATA COMMUNICATIONS

Coding Efficiency

=

Hamming Code 2 + + 1 Baud-to-Bit rate Conversion

= 2 Processing Gain

() = (/) (/) Shannon-Hartley Theorem on Information Capacity

= 2(1 + /) Aliasing Frequency

= M-ary Encoding

= 2 FSK Frequency Deviation

= | |2 FSK Minimum Bandwidth

= 2( + ) FSK Baud Rate

=

BPSK Minimum Double-Sided Nyquist Bandwidth

= QPSK Nyquist Bandwidth

= 2 8-PSK / 8-QAM Nyquist Bandwidth

= 3 16-PSK / 16-QAM Nyquist Bandwidth

= 4 Bandwidth Efficiency

= Dynamic Range

= 1.76 + 6.02() Dynamic Range

=

Dynamic Range

= 2 1 Maximum Quantization Error

= 2 Data Rate

=



-Law Companding

= ln 1 + ln(1 + ) Intersymbol Interference

= 20 log

ACOUSTICS & BROADCASTING

Sound Loudness

= 40 + 10 2() Sound Power Level (PWL)

= 1010() = 10 10 + 120

Sound Power Level from an Isotropic Source

= + 20 10 + 11 Sound Power Level from a Source at Ground Level

= + 20 10 + 8 Sound Pressure Level (SPL)

= 2010() = 20 10 + 94

Sound Intensity

= 42

Sound Intensity Level (SIL)

= 1010( ) = 10 10 + 120

Nth Decade

2 = 1 10 Reverberation Time Stephen and Bate Equation

60 = 0.0123 + 0.1070 Sabine Equation

60 = 0.161 60 = 0.161 60 = 0.049 60 = 0.049

Norris-Eyring Equation

60 = 0.161 (1 ) 60 = 0.049 (1 )

Helmholtz Resonator Frequency

= 2 f-rating

=



Alumination

= 2

Y-signal

= 0.30 + 0.59 + 0.11 I-signal

= 0.60 0.28 0.32 Q-signal

= 0.21 0.52 0.31 C-signal magnitude

= 2 + 2 C-signal phase

= 1

Video Frequency Response

= 80 Differential Gain

= 1 100 Tape Recorded Wavelength

=

Channel Frequency (Ch.2-4)

= 54 + 6( 2) Channel Frequency (Ch.7-13)

= 174 + 6( 7) Channel Frequency (Ch.14-83)

= 470 + 6( 14) Picture Carrier Frequency

= + 1.25 Sound Carrier Frequency

= + 1.25 + 4.5 Color Sub-Carrier Frequency

= + 1.25 + 3.58 Velocity of Sound in Terms of Youngs Modulus and Density

= Horizontal Scanning Time in terms of number of pixels

= 0.125

From:

ECE Solutions in Electronics Systems & Technologies (Arceo & De Vera)

Est Formulas

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