formulario de electronica.pdf
TRANSCRIPT
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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
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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
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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
Resistance, R 1.00 Ohms
Voltage, E 1.00 VPower, P 1.00 W
Resistance, R 1.00 Ohms
Current, I 1.00 A
Resistance, R 1.00 Ohms
Voltage, E 1.00 V
Power, P 1.00 W
Resistance, R 1.00 Ohms
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
Resistance, R 1.00 Ohms
Current, I 1.00 A
Power, P 1.00 W
Resistance, R 1.00 Ohms
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
Resistance, R 1.00 Ohms
Power, P 1.00 W
Voltage, E 1.00 V
Current 1.00 A
Power, P 1.00 W
Current, I 1.00 A
Resistance, R 1.00 Ohms
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
=
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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
Impedance, Z 1.00 Ohms
PF, cos 1.00 (no units)
Voltage, E 1.00 V
Power, P 1.00 W
Impedance, Z 1.00 Ohms
Current, I 1.00 A
Impedance, Z 1.00 Ohms
Voltage, E 1.00 V
PF, cos 1.00 (no units)
Power, P 1.00 W
Impedance, Z 1.00 Ohms
Voltage, E 1.00 V
PF, cos 1.00 (no units)
Current, I 1.00 A
Power, P 1.00 W
Voltage, E 1.00 V
Voltage, E 1.00 V
Impedance, Z 1.00 Ohms
Current, I 1.00 A
PF, cos 1.00 (no units)
Power, P 1.00 W
Impedance, Z 1.00 Ohms
Current, I 1.00 A
PF, cos 1.00 (no units)
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
Impedance, Z 1.00 Ohms
Power, P 1.00 W
PF, cos 1.00 (no units)
Voltage, E 1.00 V
Current, I 1.00 A
Power, P 1.00 W
PF, cos 1.00 (no units)
Current, I 1.00 A
Impedance, Z 1.00 Ohms
Power, P 1.00 W
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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 =
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Resistance, R 100.0 ohms
Reactance, X 100.0 ohms
Impedance, Z 141.4 ohms
Phase Angle 45.00 degrees
Resistance, R 10.0 ohms
Reactance, X 10.0 ohms
Impedance, Z 14.1 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
Resistance, R 20.0 ohms
Reactance, XL 20.0 ohms
Reactance, XC 20.0 ohms
Impedance, Z 20.0 ohms
Phase Angle 0.00 degrees
Inductance 643.06 uH
Frequency 11.130 kHz
Reactance 44.97 ohms
Capacitance 0.32 mF
Frequency 11.130 Hz
Reactance 44.97 ohms
Resistance 1 2.000 ohms
Resistance 2 2.000 ohms
Resistance 3 2.000 ohms
Resistance 4 2.000 ohms
Resistance 5 2.000 ohms
Resistance 6 2.000 ohms
Total 12.000 ohms
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
=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=
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Resistance, R 6800.0 ohms
Reactance, X 8640.0 ohms
Impedance, Z 5343.5 ohms
Phase Angle 38.20 degrees
Resistance, R 3300.0 ohms
Reactance 2530.0 ohms
Impedance, Z 2007.8 ohms
Phase Angle 52.52 degrees
Reactance, XL 365.0 ohmsReactance, XC 365.0 ohms
Impedance, Z MAX ohms
Phase Angle 0.00 degrees
Resistance, R 2200.0 ohms
Reactance, XL 770.0 ohms
Reactance, XC 535.0 ohms
Impedance, Z 1371.0 ohms
Phase Angle 51.45 degrees
(A)
Resistance, R1 100.0 ohms
Resistance, R2 100.0 ohms
Reactance, XL 1000.0 ohms
Reactance, XC 500.0 ohms
Impedance, Z 951.6 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
Reactance, XL 44.97 ohms
Capacitance, C 0.32 F
Frequency, F 11.130 Hz
Reactance, XC 0.04 ohms
Resistance 1 1.000 ohms
Resistance 2 1.000 ohms
Resistance 3 1.000 ohms
Resistance 4 0.000 ohms
Resistance 5 2.000 ohms
Resistance 6 2.000 ohms
Total 0.250 ohms
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
R2 & C in Parallel with L - Case (C)
PARALLEL CIRCUITS
L is the inductance in Henries
XL is the inductive reactance in Ohms
F is the frequency in Hertz
XCis the capacitive reactance in Ohms
Z is the impedance in Ohms
is the phase angle in degrees
R is the resistance in Ohms
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).
CALCULATIONS FORMULAS NOTES
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX
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
Capacitive Reactance
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
+=
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Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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
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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
PF, cos 0.985 (no units)
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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.
CALCULATIONS FORMULAS NOTES
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX
a.c. Voltage or Current
Wavelength
F is the frequency in Hertz
T is the period in seconds
F is the frequency in Hertz
T is the period in seconds
Frequency
Period
is the wavelength I metersC is the velocity of light (3x108 m/sec)
F is the frequency in Hertz
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
==
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CALCULATIONS FORMULAS NOTES
Frequency, F 25.00 kHz
Reactance, XL 44.97 ohms
Inductance, L 286.288 uH
Inductance, L 0.00 H
Frequency, F 800.000 Hz
Reactance, XL 10.05 ohms
Inductance, L 107.86 uHReactance, XL 2.640 kilohms
Frequency, F 3895.50 kHz
Inductance, L 10.00 H
Current, I 2.00 AmpsEnergy Stored 20.00 Joules
Inductance 1 2.000 uH
Inductance 2 2.000 uH
Inductance 3 2.000 uH
Inductance 4 2.000 uH
Inductance 5 2.000 uHInductance 6 2.000 uH
Total 0.333 uH
Inductance 1 1.000 mH
Inductance 2 1.000 mH
Inductance 3 1.000 mH
Inductance 4 1.000 mH
Inductance 5 1.000 mH
Inductance 6 1.000 mHTotal 6.000 mH
Reactance 1 1.000 ohms
Reactance 2 1.000 ohms
Reactance 3 1.000 ohms
Reactance 4 1.000 ohms
Reactance 5 1.000 ohms
Reactance 6 1.000 ohmsTotal 6.000 ohms
Reactance 1 1.000 ohms
Reactance 2 1.000 ohms
Reactance 3 1.000 ohms
Reactance 4 1.000 ohms
Reactance 5 1.000 ohms
Reactance 6 1.000 ohmsTotal 0.167 ohms
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells.
Inductance
Series Inductance
Parallel Inductive Reactance
Energy Stored Formula Variables:
L is the inductance in Henries
XL is the inductive reactance in Ohms
F is the frequency in Hertz
W is the energy stored in Joules
Z is the impedance in Ohms
V is the voltage in Volts
I is the current in Amps
R is the resistance in Ohms
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=
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CALCULATIONS FORMULAS NOTES
Frequency, F 11.13 mHz
Reactance, XC 44.97 ohms
Capacitance, C 317.982 pF
Capacitance, C 317.98 pF
Frequency, F 11.130 mHz
Reactance, XC 44.97 ohms
Capacitance, C 317.98 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 2 1.000 uF
Capacitance 3 1.000 uF
Capacitance 4 1.000 uF
Capacitance 5 1.000 uF
Capacitance 6 1.000 uFTotal 0.167 uF
Capacitance 1 1.000 pF
Capacitance 2 1.000 pF
Capacitance 3 1.000 pF
Capacitance 4 1.000 pF
Capacitance 5 1.000 pF
Capacitance 6 1.000 pFTotal 6.000 pF
Reactance 1 1.000 ohms
Reactance 2 1.000 ohms
Reactance 3 1.000 ohms
Reactance 4 1.000 ohmsReactance 5 1.000 ohms
Reactance 6 1.000 ohmsTotal 6.000 ohms
Reactance 1 1.000 ohms
Reactance 2 1.000 ohms
Reactance 3 1.000 ohms
Reactance 4 1.000 ohms
Reactance 5 1.000 ohms
Reactance 6 1.000 ohmsTotal 0.167 ohms
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
RETURN TO INDEX
Series Capacitive Reactance
Parallel Capacitance
Formula Variables:
C is the capacitance in Farads
Xc is the capacitive reactance in Ohms
F is the frequency in Hertz
Q is the electric charge in Coulombs
W is the energy stored in Joules
Z is the impedance in Ohms
E is the voltage in Volts
I is the current in Amps
R is the resistance in Ohms
Series Capacitance
Charge & Energy Stored
Parallel Capacitive Reactance
Capacitance
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells.
CAPACITIVE REACTANCE
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=
-
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Resistance, R 1 Ohms
Capacitance, C 1 uF
Time Const, 1 uSecTime Const, 1 uSec
Capacitance, C 1 uF
Resistance, R 1 Ohms
Time Const, 1 uSec
Resistance, R 1 Ohms
Capacitance, C 1 uF
Resistance, R 1 Ohms
Inductance, L 1 uH
Time Const, 1 uSecTime Const, 1 uSecInductance, L 1 uH
Resistance, R 1 Ohms
Time Const, 1 uSec
Resistance, R 1 Ohms
Inductance, L 1 uH
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
NOTES
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX
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 =
-
7/27/2019 Formulario de Electronica.pdf
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CALCULATIONS FORMULAS NOTES
Inductance, L 10.00 uH
Capacitance, C 100.00 pF
Frequency, F 5.033 mHz
Inductance, L 11.13 uH
Frequency, F 7.112 mHz
Capacitance, C 45.00 pF
Capacitance, C 45 pF
Frequency, F 7.112 mHz
Inductance, L 11.13 uH
Inductance, L 11.13 uH
Frequency, F 7.112 mHz
Reactance, XL 497.36 ohms
Capacitance, C 45.00 pF
Frequency, F 7.112 mHz
Reactance, XC 497.30 ohms
Reactance, X 1.00 ohms
Resistance, R 10.00 ohms
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)
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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.
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX
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)
Capacitive Reactance
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
=
-
7/27/2019 Formulario de Electronica.pdf
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CALCULATIONS FORMULAS NOTES
Inductance, L 11.13 uH
Capacitance,C 45.00 pF
Frequency, F 14.223 mHz
Inductance, L 11.13 uH
Capacitance,C 45.00 pF
Frequency, F 3.556 mHz
Inductance, L 11.13 uH
Capacitance,C 45.00 pF
Frequency, F 7.112 mHz
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
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
Half-Wave Filter Design (5-Pole)
COIL WINDING (AIR CORE)
Enter values and units of measurement in gray cells. Calculated results are displayed in yellow cells. RETURN TO INDEX
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=
-
7/27/2019 Formulario de Electronica.pdf
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Coil Radius, r 1 inches
No. of Turns, N 40 (no units)
Coil Length, l 1 inches
Inductance, L 84.21 uH
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
Inductance, L 71.37 uH
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
Frequency, F 5.890 mHz
Coil Radius, r 0.55 inches
No. of Turns, N 40Length of Coil, l 1 inches
Depth of Coil 0.1 inches
Inductance, L 29.113 uH
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
Copyright 2003-2005 XL Technologies, Inc. All Rights Reserved.
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