Formulario de Electronica.pdf

7/27/2019 Formulario de Electronica.pdf

1/22

The Electronics Toolkit provides a convenient source of calculations for the majority of

basic electronics formulas. Based on a spreadsheet format, all formulas are clearly

illustrated and include convenient features such as on the fly units conversions.

Calculators are provided in the following areas:

Ohms law for a.c. and d.c. Series Circuits

Parallel Circuits Networks

Alternating Current/Voltage Inductance and Inductive CircuitsCapacitance and Capacitive Circuits L/R and RC Time Constants

Coil Winding for Air and Toroid Cores Filter Circuits

Math for A.C. Circuits Basic Antennas

Transmission Lines Magnetic Circuits

Decibels Conversion Factors


2/22

Click on topic below to jump to desired worksheet.

Legal Notice Please do not make illegal copies - Each CD contains a unique, hidden serial number.

Calculation of resistance, voltage, current and power for parallel circuits

Kirchhoff's Voltage and Current Laws, Superposition, Thevenin, Norton and Millman Theorems

Calculation of resistance, voltage, current and power for series circuits

Ohm's Law for a.c. circuits (voltage, current, impedance, power, power factor)

Calculation of RC and L/R time constants

Capacitance

Time Constants

Calculation of rms, peak, peak-to peak, average voltage/current, frequency, period, wavelength

Inductance, energy stored in an inductor, inductive reactance, phase shift, inductive coupling

Capacitance, charge (Coulomb's Law), energy stored in a capacitor, capacitive reactance, phase shift

Low pass, high pass, band pass (constant-k, m-derived), resonant filter

Rectangular coordinates, polar coordinates, rectangular-to-polar conversion, polar-to-rectangular conversion

Filters

Complex Math for A.C.Half-wave dipole, quarter-wave vertical, folded dipole, 3-element yagi, range calculations

Resistor/capacitor color codes, wire chart, toroid data, resistance of cylindrical conductors, T.C. of resistance

Basic Antennas

Component Data

Magnetic flux, magnetic field intensity, permeability, series magnetic circuit, hysteresis

Calculation of power, voltage, and current gain/loss

Magnetic Circuit s

Decibels

Impedance, inductance, capacitance, attenuation for coax and ladder transmission lines

Units, symbols, and definitions for electric, magnetic, and electromagnetic variables

Transmission Lines

Basic Units & Conversions

Coil Winding (air core)

Basic Formulas (d.c.)

Basic Formulas (a.c.)

Basic Series Circuits

Basic Parallel Circuits

Networks

Al tern ating Cur rent /Volt age

Inductance

General Notes:

1. The Toolkit worksheets are set to a default screen resolution of 800x600 pixels. For other screen resolutions, click on 'View'

and set 'Zoom' at the desired percentage for best viewing.

2. For best results when printing worksheets, set printer resolution at 600dpi if available on your printer. For draft quality, set printer

resolution to 300dpi.

3. Version 1.0.2 02-21-2005

Copyright 2003-2005 XL Technologies, Inc. All Rights Reserv

TOPIC DESCRIPTION

Ohm's Law for d.c. circuits (voltage, current, resistance, power)

Coil Winding (toroids) Calculation of inductance, capacitance, resonant frequency, no. of turns for toroid core single layer coils

Series/parallel resonance, resonant frequency, inductive/capacitive reactance, Q-factor, bandwidth

Calculation of inductance, capacitance, resonant frequency, no. of turns for air core single/multi-layer coils

Resonance


3/22

Voltage, E 1.00 V

Current, I 1.00 A

Resistance, R 1.00 Ohms

Power, P 1.00 W

Current, I 1.00 A


Voltage, E 1.00 VPower, P 1.00 W


Current, I 1.00 A


Voltage, E 1.00 V

Power, P 1.00 W


Voltage, E 1.00 V

Current, I 1.00 A

Power, P 1.00 W

Voltage, E 1.00 V

Voltage, E 1.00 V


Current, I 1.00 A

Power, P 1.00 W


Current, I 1.00 A

Voltage, E 1.00 V

Power, P 1.00 W

Current, I 1.00 A

Voltage, E 1.00 V


Power, P 1.00 W

Voltage, E 1.00 V

Current 1.00 A

Power, P 1.00 W

Current, I 1.00 A


Power, P 1.00 W

Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.

Space For User Notes:

RETURN TO INDEXEnter values and units of measurement in gray cells. Calculated results are displayed in yellow cells.

Ohm's Law - Calculate Power

NOTES

Ohm's Law - Calculate Resistance

Coulomb (C) - The basic unit of electric charge is the coulomb (C) named after Charles A. Coulomb. When a current of one ampere is maintained for one second, a

charge of one coulomb flows past a given point. It is equivalent to a charge of 6.25x1018

electrons.

Ohm's Law - In 1827, Dr. George S. Ohm discovered that the current through a conductor is directly proportional to the difference of potential (voltage) across the

circuit. According to ohm's Law, a potential difference of one volt across a one ohm resistance will cause a current of one amp to flow through the resistance. Stated

as a formula, the ratio of volts to amps is a constant called resistance (R) and is measured in ohms ().Voltage (E or V) - The voltage between two points in a circuit is called the potential difference or electromotive force (emf) and is measured in volts (V) (named after

Count Alessandro Volta).

Current (I) - The current through a circuit is the rate of flow of electric charge and is measured in amperes (A) (named after Andre-Marie Ampere).

Resistance (R) - Resistance impedes the flow of current and is measured in ohms ().Power (P) - Power is the rate at which work is done (work per unit time) or energy produced/consumed in watts (W). The power consumed in a circuit

device is the work/charge multiplied by the charge/time or P=V*I watts. (For d.c. circuits, volt-amps and watts are equivalent in magnitude).

Note: In d.c. circuit diagrams and calculations, conventional (positive to negative) current flow is assumed.

CALCULATIONS FORMULAS

Ohm's Law - Calculate Voltage

Ohm's Law - Calculate Current

Practical Units and Conversions:

Coulomb = 6.25 x 1018

electrons.

Ampere = coulomb/second

Volt = joule/coulomb

Watt = joule/second

Ohm = volt/ampere

Siemens* = ampere/volt

*Originally the 'mho' for conductance.

I

ER =

2I

PR =

PER

2=

IRE =

PRE =

I

PE =

R

EI =

R

PI =

E

PI =

R

EP

2

=

EIP =

RIP2

=


4/22

Voltage, E 1.00 V

Current, I 1.00 A

Impedance, Z 1.00 Ohms

PF, cos 1.00 (no units)

Power, P 1.00 W

Current, I 1.00 A



Voltage, E 1.00 V

Power, P 1.00 W


Current, I 1.00 A


Voltage, E 1.00 V


Power, P 1.00 W


Voltage, E 1.00 V


Current, I 1.00 A

Power, P 1.00 W

Voltage, E 1.00 V

Voltage, E 1.00 V


Current, I 1.00 A


Power, P 1.00 W


Current, I 1.00 A


Voltage, E 1.00 V

Power, P 1.00 W

Current, I 1.00 A

PF, cos 1.00 (no units)Voltage, E 1.00 V


Power, P 1.00 W


Voltage, E 1.00 V

Current, I 1.00 A

Power, P 1.00 W


Current, I 1.00 A


Power, P 1.00 W


Resistance, R = Z cos

cos = R/Z

Phase Angle, = cos-1

(R/Z)

Reactance, X = Z sin

sin = X/Z

Phase Angle, = sin-1

(X/Z)

Note: See Series and Parallel Circuits work sheets

to calculate values for a.c. impedance, Z. and the

phase angle, .

Ohm's Law - Calculate Current

Ohm's Law - Calculate Impedance

Ohm's Law - Calculate Voltage

RETURN TO INDEX

NOTESCALCULATIONS FORMULAS

Apparent Power, Papp = EI (volt-amps)

Real Power, Preal = EI cos (watts)

Reactive Power, Preactive=EI sin (VAR)

Power factor, PF = cos = Preal/Papp

Phase Angle, = cos-1

(Preal/Papp)

Ohm's Law - Calculate Power

DEFINITIONS:

Voltage (E or V) - Generally, the voltage in a.c. circuits is the 'root mean squared' (RMS) or 'effective' voltage, measured involts (V).

Current (I) - Similarly, the current in a.c. circuits is the RMS value or effective value, measured inamperes (A).

Impedance (Z) - Impedance is the total opposition to the flow of an alternating current and it may consist of any combination of resistance, inductive reactance, and

capacitive reactance. Like resistance in d.c. circuits, it is measured inohms ().Power (P) - Real Power (as opposed to apparent or reactive) is the power in watts (W) dissipated in heat through resistance.

Power Factor (PF) - PF is the ratio of the true power (watts) to the apparent power (volts x amps). It is expressed as the cosine of the phase angle (cos ) or in a.c.

power applications, the cos is multiplied by 100 and expressed as a percentage.

Phase Angle () - This is the angular difference in time between corresponding values in the cycles of two wave forms of the same frequency (i.e. voltage and current in

an a.c. circuit containing inductance, resistance and capacitance).

Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells.

I

EZ =

cos2I

PZ =

PEZ cos

2

=

IZE =

cos

PZE =

cosI

PE =

Z

EI =

cosZ

PI =

cosE

PI =

Z

EP

cos2

=

cosEIP =

cos2ZIP =


5/22

Resistance, R 100.0 ohms

Reactance, X 100.0 ohms

Impedance, Z 141.4 ohms

Phase Angle 45.00 degrees





Reactance, XL 30.0 ohms

Reactance, XC 31.0 ohms

Impedance, Z -1.0 ohms

Phase Angle -90.00 degrees






Inductance 643.06 uH

Frequency 11.130 kHz

Reactance 44.97 ohms

Capacitance 0.32 mF

Frequency 11.130 Hz


Resistance 1 2.000 ohms






Total 12.000 ohms


=0 when XL = XC (resonance)

Note: If the series circuit contains less

than six resistors, enter 0 for the

remaining resistances.

SERIES CIRCUITS

L is the inductance in Henries

XLis the inductive reactance in Ohms

F is the frequency in Hertz

XC is the capacitive reactance in Ohms

Z is the impedance in Ohms

is the phase angle in degrees

R is the resistance in Ohms

If the series circuit consists of series capacitors only, the impedance, Z, is equal to the sum of the individual

capacitive reactances. The phase angle, , is equal to -900

(The voltage lags the current by 900).

If the series circuit consists of series inductors only, the impedance, Z, is equal to the sum of the individual

inductive reactances. The phase angle, , is equal to +900

(The voltage leads the current by 900).

An easy way to remember the phase relationship of voltage/current in inductive and capacitive circuits is: "eLi

the iCe man". (i.e.voltage leads in inductive circuits and current leads in capacitive circuits).

RT = R 1 +R2 +R3 +Rn

CALCULATIONS FORMULAS NOTES

L & C in Series

R, L, & C in Series

Inductive Reactance

Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX

R & L in Series

R & C in Series

Capacitive Reactance

Series Resistance

22

LXRZ +=

CL XXZ =

22 )(CL

XXRZ +=

22

C

XRZ +=

R

XL

arctan=

R

XC

arctan=

RXX CL = arctan

FLXL 2=

FCX

C

2

1=


6/22









Reactance, XL 365.0 ohmsReactance, XC 365.0 ohms

Impedance, Z MAX ohms







(A)

Resistance, R1 100.0 ohms

Resistance, R2 100.0 ohms




Phase Angle -62.60 degrees (B)

Impedance, Z ohms

Phase Angle degrees

Impedance, Z ohms

Phase Angle degrees (C)

Inductance, L 643.06 uH

Frequency, F 11.130 kHz


Capacitance, C 0.32 F

Frequency, F 11.130 Hz








Total 0.250 ohms


R2 & C in Parallel with L - Case (C)

PARALLEL CIRCUITS


XL is the inductive reactance in Ohms


XCis the capacitive reactance in Ohms


is the phase angle in degrees


If XL - XC is positive, the circuit is inductive.

If XL - XC is negative, the circuit is capacitive.

An easy way to remember the phase relationship of voltage/current in inductive and capacitive circuits is: "eLi the iCe

man". (i.e. voltage leads current in inductive circuits and current leads voltage in capacitive circuits).



Note: Diagrams (B) & (C) above are

special cases of (A). For (B), enter "0"for Resistance R2. For (C), enter "0"

for Resistance R1.

=00

when XL = XC (resonance)

Parallel Resistance


R1&L in Parallel with R2&C - Case (A)

Inductive Reactance

R1 & L in Parallel with C - Case (B)

R & L in Parallel

R & C in Parallel

L & C in Parallel

R, L, & C in Parallel

22

*

C

C

XR

XRZ

+

=

22

*

L

L

XR

XRZ

+

=

CL

CL

XX

XX

Z

=

*

LX

Rarctan=

CX

Rarctan=

=

CL

CL

XX

XXR

*

)(arctan

FLXL 2=

FCX

C

2

1=

n

T

RRR

R1

...11

1

21

++

=

2221

22

2

22

1

)()(

))((

CL

CL

XXRR

XRXRZ

++

++=

)()(

)()(tan

2212

2221

22

1

22

21

LC

LCCL

XRRXRR

XRXXRX

+++

++=

22

1

22

1

)(CL

L

C

XXR

XRXZ

+

+

=

2

1

2

1

21tan

C

LCL

XR

RXXX =

22

2

22

2

)(CL

C

L

XXR

XRXZ

+

+

=

2

2

2

2

2

1tan

L

CCL

XR

RXXX =

2222 )(

**

CLCL

CL

XXRXX

XXRZ

+=


7/22


Note: Due to the infinite number of circuit configurat ions, no calculations are presented, only the prinicples and methods of network solutions are

presented. Calculations from other worksheets may be used to reduce networks to equivalent values.

RETURN TO INDEX

Kirchhoff's Voltage Law

The algebraic sum (for d.c. circuits) or the phasor

sum (for a.c. circuits) of the source voltages and

voltage drops around a closed electric circuit (loop) is

zero.

DEFINITIONS NOTES

Kirchhoff's Current Law

The algebraic sum (for d.c. circuits) or the phasor

sum (for a.c. circuits) of the currents in and out of a

node (point) is zero.

Thevenin's Theorem for d.c (or a.c.) Circuits

Any two terminal network of resistors (or impedances)

and voltage sources is equivalent to a single resistor

(or impedance) in series with a single constant

voltage source.

Norton's Theorem for d.c. (or a.c.) Circuits

Any two terminal network of resistors (or impedances)

and current sources is equivalent to a single resistor

(or impedance) in parallel with a single constant

current source.

Millman's Theorem

Any number of constant current sources that are

directly connected in parallel can be converted to a

single current source whose total output is the

algebraic sum (for d.c.) or the phasor sum (for a.c.) of

the individual source currents, and whose total

internal resistance (or impedance) is the result of

combining the individual source resistances (or

impedances) in parallel.

Superposition Theorem

In a network of linear resistances (or impedances)

containing more than one source, the resultantcurrent flow at any one point is the algebraic sum (for

d.c.) or the phasor sum (for a.c.) of the current that

would flow at that point if each source is considered

separately, and all other sources are temporarily

replaced by their equivalent internal resistances (or

impedances). This would involve replacing each

voltage source by a short-circuit and each current

source with an open circuit.

=+++ 0...321 nEEEE

=+++ 0...321 nIIII


8/22

Period, T 1 mSec

Frequency, F 1 kHz

Frequency, F 1 KHz

Period, T 0.001 Sec

Frequency, F 3.75 Mhz

Wavelength, 80 Meters

Avg 123.000 V

Peak 193.233 V

Peak-Peak 386.712 V

RMS 136.653 V Degrees Rad Sin Voltage

00 0 0 0.0%

Peak 120.000 uA 450 /4 0.707 70.7% rms

Peak-Peak 240.000 uA 600 /3 0.866 86.6%RMS 84.840 uA 90

0 /2 1 100.0% peak

Avg 76.440 uA 1800 0 0.0%

Peak-Peak 240.000 mV

RMS 84.720 mV

Avg 76.320 mV

Peak 120.000 mV

RMS 84.720 mA

Avg 76.163 mA

Peak 119.794 mA

Peak-Peak 239.588 mA

Phase Angle 10.00 Degrees

Voltage, E 120.00 V

Current, I 10.00 A

Power, PREAL 1181.769 W

Apparent Power 1200.000 VA

Reactive Power 208.378 VAR



Calculate Power

Sine Wave Characteristics

Primary Relationships

peak = 0.500*peak-peak

avg = 0.899*rms

peak = 1.414*rms

peak-peak = 2.828*rms

rms = 0.707*peak

avg = 0.637*peak

rms = 0.353*peak-peak

avg = 0.318*peak-peak

rms = 1.111*avg

peak = 1.571*avg

peak-peak = 3.144*avg

peak-peak = 2.000*peak

Amplitude - The amplitude of a periodic curve (in electronics, typically a sinusoidal wave) is taken as the maximum displacement or value of the curve.

Frequency - The number of complete cycles occurring in a periodic curve in a unit of time is called the frequency (F) of the curve.

Period - The time (T) required for a periodic function, or curve, to complete one cycle is called the period.

Phase Angle - The angular difference () between two curves or waves is called the phase angle.

RMS - The effective value of a sine wave of current can be calculated by taking equally space samplings and extracting the the square root of their mean, or

average, values.

Peak - The maximum instantaneous value of an alternating quantity such as voltage or current.

Peak-Peak - The amplitude of an alternating quantity measured from positive peak to negative peak.

Average Value - The average of many instantaneous amplitude values taken at equal intevals of time during a half cycle of alternating current. The average value

of a pure sine wave during one half cycle is 0.637 times its maximum or peak value.



a.c. Voltage or Current

Wavelength


T is the period in seconds


T is the period in seconds

Frequency

Period

is the wavelength I metersC is the velocity of light (3x108 m/sec)


Note: Conversion factors are for

sine waves only

TF

1=

FT

1=

F

C=

EIPAPPARENT=

sinEIPREACTIVE=

cosEIPREAL =

cos=PF

peak

peakV

VVrms 707.0

2==

pea kpea kavg VVV 637.02

==


9/22





Inductance, L 0.00 H

Frequency, F 800.000 Hz


Inductance, L 107.86 uHReactance, XL 2.640 kilohms


Inductance, L 10.00 H

Current, I 2.00 AmpsEnergy Stored 20.00 Joules

Inductance 1 2.000 uH




Inductance 5 2.000 uHInductance 6 2.000 uH

Total 0.333 uH

Inductance 1 1.000 mH





Inductance 6 1.000 mHTotal 6.000 mH

Reactance 1 1.000 ohms





Reactance 6 1.000 ohmsTotal 6.000 ohms








INDUCTIVE REACTANCE

Inductive Reactance

RETURN TO INDEX

DEFINITIONS:

Inductance, L - Inductance is the ability of a conductor to produce an induced voltage as the current in the conductor is varied. Typically inductors take the form

of a coil of wire that concentrates the magnetic flux lines thereby increasing the inductance. The unit of inductance is the Henry - the amount of inductance which

will induce a counter EMF of one volt when the inducing current is varied at the rate of one ampere per second.

Inductive Reactance, XL - This is the characteristic of an inductor to impede the flow of a.c. current. The higher the inductive reactance, the more the a.c. curent

is impeded (just as resistance impedes the flow of current in a d.c. circuit). An important characteristic of inductive reactance is that it increases as the frequency

is increased (just the opposite of capacitive reactance).

Energy Stored, W - An inductor stores energy in the electric field, since an electric current is induced back into the conductor by the decaying magnetic field.

The amount ofenergy stored in an inductor (Joules) is directly proportional to the inductance and the square of the current.

Frequency


Inductance

Series Inductance

Parallel Inductive Reactance

Energy Stored Formula Variables:


XL is the inductive reactance in Ohms


W is the energy stored in Joules


V is the voltage in Volts

I is the current in Amps


Parallel Inductance

Series Inductive Reactance

FLXL

2=

LXF L

2=

2)2/1( LIW =

nTLLLL ...

21++=

n

T

LLL

L1

...11

1

21

++

=

nTXXXX ...21 ++=

n

T

XXX

X1

...11

1

21

++

=

F

XL

L

2=


10/22


Frequency, F 11.13 mHz


Capacitance, C 317.982 pF





Reactance, XC 44.970 ohmsFrequency, F 11.13 mHz

Capacitance, C 5.00 mF

Voltage, E 100.00 VoltsEnergy Stored 25.00 Joules

Charge, Q 0.50 Coulombs

Capacitance 1 1.000 uF





Capacitance 6 1.000 uFTotal 0.167 uF

Capacitance 1 1.000 pF





Capacitance 6 1.000 pFTotal 6.000 pF




Reactance 4 1.000 ohmsReactance 5 1.000 ohms









RETURN TO INDEX

Series Capacitive Reactance

Parallel Capacitance

Formula Variables:

C is the capacitance in Farads

Xc is the capacitive reactance in Ohms


Q is the electric charge in Coulombs

W is the energy stored in Joules


E is the voltage in Volts

I is the current in Amps


Series Capacitance

Charge & Energy Stored

Parallel Capacitive Reactance

Capacitance


CAPACITIVE REACTANCE


Frequency

DEFINITIONS:

Capacitance, C - This is the ability of a dielectric to store an electric charge which is measured in Farads (after Michael Faraday). Physically, a capacitor

consists of a dielectric material between two conductors. In operation, d.c. voltages are blocked while a.c. voltages pass through.

Capacitive Reactance, Xc - This is the characteristic of a capacitor to impede the flow of a.c. current. The higher the capacitive reactance , the more the a.c.

curent is impeded (just as resistance impedes the flow of current in a d.c. circuit). An important characteristic ofcapacitive reactance is that it increases as the

frequency is decreased (just the opposite of inductive reactance).

Charge, Q - When a voltage is applied to opposing plates of the capacitor, negative and positive electric charges build up creating a field that stresses the

dielectric. The higher the voltage, the more the dielectric is stressed and the higher the charge (in Coulombs).

Energy Stored, W - The amount ofenergy stored in a capacitor (Joules) is directly proportional to the capacitance and the square of the voltage.

n

T

XXX

X1

...11

1

21

++

=

nTXXXX ...21 ++=

nTCCCC ...21 ++=

n

T

CCC

C1

...11

1

21

++

=

2)2/1( CEW =CEQ =

CCX

F

2

1=

FCX

C

2

1=

CFX

C2

1=


11/22

Resistance, R 1 Ohms

Capacitance, C 1 uF

Time Const, 1 uSecTime Const, 1 uSec

Capacitance, C 1 uF


Time Const, 1 uSec


Capacitance, C 1 uF


Inductance, L 1 uH

Time Const, 1 uSecTime Const, 1 uSecInductance, L 1 uH


Time Const, 1 uSec


Inductance, L 1 uH


NOTES


RC & L/R TIME CONSTANTS

t - The time constant in seconds

L - the inductance in henries

C - The capacitance in farads

R - The resistance in ohms

The time constant is the time, in seconds, that it takes a voltage across a capacitor or for the current through an

inductor to build up to 63.2% of its final value.

The Time Constant is also the time, in seconds, that it takes the voltage across a capacitor or the current through an

inductor to discharge to 36.8% of its initial value.

A long time constant takes approximately 5 time constants to build up to 99% of its final value.

A short time constant is defined as one-fifth or less the pulse width, in time, for the applied voltage.

RC Time Constant

L/R Time Constant

CALCULATIONS FORMULAS

CR *=

CR

=

RC

=

R

L=

RL *=

LR =


12/22








Capacitance, C 45 pF











Series Q 0.10 (no units)

Parallel Q 10.00 (no units)

Resonant Freq., FR 7.112 mHz

Q-Factor 150.00 ohmsDelta F 0.047 mHz

Frequency, F1 7.088 mHz

Frequency, F2 7.136 mHz

Frequency, Fr 1.00 ohmsBandwidth, F 10.00 ohms

Q-Factor 0.10 (no units)


Frequency

Inductance

Capacitance

DEFINITIONS:

Resonant Frequency - In an LC circuit, the resonant frequency occurs when the inductive and capacitive reactances are equal and opposite, such that X c = XL.

Resonance - In an LC circuit, as the frequency is increased, the inductive reactance increases and the capacitive reactance decreases. Due to these opposing

characteristics, there is a frequency where the inductive and capacitive reactances are equal to each other. This condition is called resonance and the circuit is

called a resonant circuit .

Q Factor- The ratio of the reactance (capacitive or inductance) to the device's resistance is known as the Q Factor or figure of merit .

Bandwidth - The width of the resonant band of frequencies with a response of 70.7% of the magnitude and centered around the resonant frequency (Fr) is called the

bandwidth of the tuned circuit.


Formula Variables:

L is the inductance, Henries

C is the capacitance, Farads

R is the resistance, Ohms

X is the reactance (XL or Xc), Ohms

F is the frequency, Hertz

Q is the ratio of X to R, no units

Z is the impedance, Ohms

Series RLC Circuit @ Resonance:

Z = R

Xc = XL

Phase Angle = 0

Power Factor = 1

Z = Min

I = Max

Vo = Min

Parallel RLC Circuit @ Resonance:

Z = R

Xc = XL

Phase Angle = 0

Power Factor = 1

Z = Max

I = Min.

Vo = Max.

Bandwidth

Q Factor (Components)

(series circuits) (parallel circuits)

Q Factor (Resonant Circuit)


Inductive Reactance

LCF

2

1=

LFC

224

1

=

CFL

224

1

=

FLXL 2=

FCX

C

2

1=

LorC

LorC

X

R

R

XQ ==

21 FFQ

FF r ==

21

F

FF r

=

22

FFF

r

+=

F

FQ R

=


13/22



Capacitance,C 45.00 pF








Frequency, F 13.5 MHz

Load 50 ohms

Cutoff Freq. 15.255 MHz

Inductance, L1 0.52 uH

Inductance, L2 0.52 uH

Capacitance, C1 208.66 pF

Capacitance, C2 417.32 pFCapacitance, C3 208.66 pF


Half-Wave Filter Design (5-Pole)

COIL WINDING (AIR CORE)


DEFINITIONS:

Filter - A network that is designed to attenuate certain frequencies, but pass other frequencies, is called a filter.

Bands - A filter possesses at least one pass band and at least one stop band.

Stop Band - A band of frequencies for which the attenuation is theoretically infinite.

Pass Band - A band of frequencies for which the attenuation is theoretically zero.

Cutoff Frequency - The frequencies that separate the various pass and stop bands are called cutoff frequencies.

Low Pass Filters - Cutoff Frequency

Band Pass Filters - Center Frequency

High Pass Filters - Cutoff Frequency

LCFcutoff

1=

LCFcutoff

4

1=

LCFcenter

2

1=


14/22

Coil Radius, r 1 inches

No. of Turns, N 40 (no units)

Coil Length, l 1 inches


Spacing 40 TPI

Typ. Wire Size 22 AWG

Coil Dia., d 3 inches

No. of Turns, N 60 (no units)

Length of Coil, l 10 inches


Spacing 6 TPI

Typ. Wire Size #N/A AWG

Coil Radius, r 0.25 inches TPI TPI

Length of Coil, l 1 inches AWG enameled inches mm insulated

Inductance, L 8.16 uH 10 9.6 0.1019 2.59

No. of Turns, N 39.99 (no units) 12 12.0 0.0808 2.05

Spacing 40.0 TPI 14 15.0 0.0641 1.63

Wire Size 22 AWG 16 18.9 0.0508 1.29

17 21.2 0.0453 1.15

18 23.6 0.0403 1.02 13.3

19 26.4 0.0359 0.91

Coil Dia., d 0.5 inches 20 29.4 0.0320 0.81

Length of Coil, l 1 inches 21 33.1 0.0285 0.72

Inductance, L 8.16 uH 22 37.0 0.0254 0.64

No. of Turns, N 39.99 (no units) 23 41.3 0.0226 0.57

Spacing 40.0 TPI 24 46.3 0.0201 0.51

Wire Size 22 AWG 25 51.7 0.0179 0.45

26 58.0 0.0159 0.40

27 64.9 0.0142 0.36

28 72.7 0.0126 0.32

Inductance, L 107.85 uH 29 81.6 0.0113 0.29

Capacitance, C 6.77 pF 30 90.5 0.0100 0.25


Coil Radius, r 0.55 inches

No. of Turns, N 40Length of Coil, l 1 inches

Depth of Coil 0.1 inches


Dia. Of Wire, d 0.001 cm

Length of Wire, l 200 cm

Induct. L (low freq) 2.061 uH

Induct. L (high freq) 1.961 uH


Diameter

Formula Variables:

L is the inductance, Henries

r is the coil radius, inches

d is the coil diameter, inches

l is the coil length, inches

N is the number of turns

b is the depth of coil winding for multi-layer coils*

TPI is the number of turns per inch

AWG is the American Wire Gauge standard

C is the Capacitance

F is the Frequency

* These formulas are based on short coils (i.e. length

Formulario de Electronica.pdf

Documents

Transcript of Formulario de Electronica.pdf