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Click on the following bookmarks for further details of a Capacitance/Inductance Tool:

Capacitance and Inductance of assorted structures
Impedance of Capacitance/Inductance
Self-Resonant frequency of L-C circuits
Inductor Q Factor
between parallel wires
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    Farads
    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.

Parplate.gif (4111 bytes)

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:

Coax.gif (3996 bytes)

  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.

Cwire1.gif (4345 bytes)

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.

Cwire2.gif (5286 bytes)

    Inductance of a Long Straight Round Wire is calculated from:

            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.

Selfl.gif (3218 bytes)

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.

Selfl2.gif (3348 bytes)

    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.

Wirel.gif (3766 bytes)

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     ohms

    where f is the frequency, C the capacitance and L the inductance. The versatile data entry form is shown below.

Impedan.gif (6701 bytes)

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.

Cap-g.gif (7988 bytes)

Self-resonant 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 follows:

            Q = ( 2 * Pi * f * L ) / R

    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:

Selfres.gif (5661 bytes)

Crosstalk 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.

Cross-f.gif (8519 bytes)

    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.

Crostalk.gif (4651 bytes)

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.

Cross-g.gif (8022 bytes)

    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 calculations

    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:

Toroid.gif (10544 bytes)


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