011/100 Example 1.5-1 Single Layer Capacitor

100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
Michael Benker
Example 1.5-1 Consider the design of a single layer capacitor from a dielectric that is 0.010 inches thick and has a dielectric constant of three. Each plate is cut to 0.040 inches square. Calculate the capacitor value and its Q factor.

Capacitance formed by a dielectric material between two parallel plate conductors:

C = (N-1)(KAεr/t)(FF) pF

A: plate area
εr: relative dielectric constant
t: separation
K: unit conversion factor; 0.885 for cm, 0.225 for inches
FF: fringing factor; 1.2 when mounted on microstrip
N: number of parallel plates

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004/100 Example 1.3-1B Parasitic Elements of a Physical Resistor vs. Frequency

100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
Michael Benker
Example 1.3-1B: Plot the impedance of a 5 Ω leaded resistor in ADS over a frequency range of 0 to 2 GHz.

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This indicates a resonance at 500 MHz. This is due to the parasitic iductance and capacitance that exists on a real resistor. The resistor behaves as a combination of series parasitic inductance and resistance, in parallel with a parasitic capacitance.

The impedance of an inductor is reduced as the frequency increases, while the impedance of a capacitor increases as the frequency increases. The intersection frequency of these two patters meet is the resonant frequency.

The resonance frequency can be found from equating XL and XC. The formula is:

Resonant frequency fR = 1/(2*pi*sqrt(LC))

002/100 Example 1.2-4 Skin Effect and Flat Ribbons

100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
Michael Benker
Example 1.2-4 Calculate the inductance of the 3 inch Ribbon at 60 Hz, 500 MHz, and 1 GHz. Make the ribbon 100 mils wide and 2 mils thick.

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The flat ribbon inductance is calculated with the following equation:

L = K*l*[ ln((2*l)/(W+T))+0.223*(W+T)/l + 0.5 ] nH

l: length of the wire
K: 2 for dimensions in cm and K=5.08 for dimensions in inches
W: the width of the conductor
T: the thickness of conductor

 

001/100 Example 1.2-1 Reactance and Inductance with respect to Frequency

100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
Michael Benker
Example 1.2-1: Calculate the reactance and inductance of a three inch length of AWG #28 copper wire in free space at 60 Hz, 500 MHz, and 1 GHz.

 

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> The increase in reactance with respect to frequency represents the skin effect property, in which, as the frequency increases, the current density begins to be concentrated on the surface of a conductor.