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Click on the following bookmarks for further details of a Capacitance/Inductance Tool:
Inductance of assorted structures
frequency of L-C circuits
Inductor Q Factor
Crosstalk between parallel
Inductance and flux density
of toroidal inductors
Capacitance of various Structures
Parallel Plate capacitance is calculated from the basic formula:
C = (Eo * Er * A) / d
where Eo is the permittivity of free space, and Er is the relative
dielectric constant. A is the area of a plate, and d is the separation between the plates.
A pull-down list of the dielectric constants of a range of materials is provided for
convenience. The data entry form for the parallel plate capacitor tool is shown below.
Capacitance may be calculated for both rectangular plates and round plates.
Coaxial Line capacitance is calculated from the formula:
C = 2 * Pi * Eo * Er *
loge ( ro / ri ) * Length Farads
where ro is the inside radius of the outer cyclinder, and ri is the
outside radius of the inner cylinder. The data entry form is shown below:
Parallel Wires without a Ground Plane. The capacitance of this
arrangement is calculated from:
C = Pi * Eo * Er * loge
( D / r ) * Length Farads
where Eo is the permittivity of free space, Er is the relative
dielectric constant, D is the separation between the wires, and r is the wire radius. A
pull-down list of the dielectric constant of a range of commonly available materials is
available. Note that D must be much larger than r. The data form is shown below.
Parallel Wires suspended over a Ground plane.
Crosstalk due to capacitive coupling can be greatly reduced by bringing
parallel wires near to a ground plane. The Crosstalk Tool in the PCB Menu analyses this
situation in detail, but the actual capacitance details are presented here.The capacitance
between wires is known as the mutual capacitance, and is specific to the case where the
ground plane forms the return paths of the two wires.
The data form is shown below.
Inductance of a Long Straight Round Wire is calculated
L = [0.2 * l * ( loge
( 4 * l /d ) - 0.75 ] nH
where l is the wire length in mm, and d is the diameter. The length l
must be much greater than d. The data entry form is shown below.
Inductance of a Long Straight Rectangular Strip is calculated from:
L = 0.2 * l * ( 0.5 +
loge ( 2 * l / (w+h) ) + 0.11 * ( w + h ) / l ) nH
where l is the strip length in mm, w the width and h the height. The
length l of the strip must be much larger than its width and height. The data entry form
is shown below.
Inductance of Straight Parallel Wires carrying
equal and opposite currents is calculated from:
L = 0.1 + ( 0.4 * loge
( D / r ) ) microhenries/metre
where D is the separation, and r is the wire radius, and D >> r.
Capacitor impedance Zc
and Inductor impedance Zl are calculated from the following basic equations:
Zc = 1 / ( 2 * Pi * f *
C ) ohms
Zl = 2 * Pi * f * L
where f is the frequency, C the capacitance and L the inductance. The
versatile data entry form is shown below.
Capacitance units can be set to pF, nF or uF, and inductance units can be
uH or mH. Frequency units can be kHz or MHz. Impedance versus frequency can be plotted,
and up to five sets of data can be created. Capacitor or inductor impedance can be
plotted, or a series or parallel combination of the two. A typical plot is shown below.
The plot shows the impedance curves of five capacitors of capacitance 10nF, 50nF, 100nF,
200nF and 300nF, as curves 1 to 5 respectively.
frequency of a capacitor/inductor combination is calculated as follows:
Fsrf = 1 / ( 2 * Pi *
(L * C ) 0.5 ) Hz
where L and C are the inductance and capacitance values respectively.
The Q factor of an inductor is calculated as
Q = ( 2 * Pi * f * L )
where f is the frequency of interest, L is the inductance, and R is the
effective series resistance of the inductor at that frequency.
The SRF and Q data entry form is shown below:
between parallel wires
The crosstalk tool calculates the crosstalk between two parallel
long wires, whose separation is much greater than their radii. Crosstalk is calculated
with the wires without a ground plane, and with the wires suspended over a ground plane.
Both magnetic and capacitive coupling calculations are made.
Although both coupling modes exist together, the tool makes a
separate calculation for each mode, to facilitate comparison, and to show which coupling
mode is dominant. A spot calculation is made at the selected frequency, and a plot can be
made showing all four coupling levels i.e. coupling by mutual inductance and by
capacitance, with and without a ground plane. The circuit arrangement is shown below, and
both Source and Victim source and load resistances may be defined. The crosstalk ratio
calculated is the the RlVictim voltage against VSource.
Considerable reductions in capacitively coupled crosstalk are provided by the proximity
of a ground plane, which tends to be prevalent at higher circuit impedances. Smaller
reductions in magnetically coupled crosstalk, which increase with reducing system
impedance, are provided by a ground plane. Note that the proximity of further conductors
will affect crosstalk levels.
A typical plot is shown above; Curves 1 and 2 are the capacitive
coupling with and without a ground plane respectively. Curves 4 and 3 show the magnetic
coupling with and without a ground plane. System impedance is 50 ohms throughout. The two
1metre long wires are 0.8mm diameter, 10mm apart and suspended 4mm above the ground plane.
Toroidal Inductor design
Toroidal inductors provide useful rf chokes, producing virtually no
external flux. The tool calculates the number of turns required to produce the required
inductance, for the selected core and permeability. Some commonly available core sizes are
offered in a pull-down list, or any value of core size may be entered.
If a wire size, plus any film insulation is entered, the volume of
copper is calculated, assuming a 70% area fill, and compared to the inside diameter of the
core. If less than 50% of initial ID remains, a warning is issued, as a residual hole must
be left for the winding machine's tool.
If the inductor is carrying a 50Hz current, the resulting flux density
and magnetising force can be calculated, and compared to manufacturer's data on
permeability vs flux density. Note that ac core losses are not calculated, and the power
quoted is due only to the dc resistance of the windings. Even if the user is not
attempting to design his own toroidal inductor, the tool still provides a useful guide to
inductor size for a given inductance. The data entry form is shown below: