Parametric devices in microwave, Exercises of Microwave Engineering and Acoustics

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Parametric Devices

• Uses non linear reactance or time varying reactance
• Parametric term is derived from parametric

excitation, since the capacitance or inductance, which

is a reactive parameter , can be used to produce

capacitive or inductive excitation.

• Parametric excitation is subdivided into parametric

amplification and oscillation.

• Many of the essential properties of non linear

energy storage systems were described by Faraday

and Lord Rayleigh.

In 1957 Suhl proposed a microwave solid state

amplifier that used ferrite.

The first realization of a microwave parametric

amplifier was made by Weiss in 1957 after which

the parametric amplifier was last discovered.

At present the soild state varactor diode is the

most widely used parametric amplifier.

Unlike microwave tubes, transistors and lasers, the

parametric diode is of reactive nature and thus

generates a very small amount of Johnson (thermal)

noise.

Parametric amplifier utilizes an ac rather than a dc

power supply as microwave tubes do. In this

respect, the parametric amplifier is analogous to

the quantum amplifier laser or maser in which an ac

power supply is used.

i.e

C(v) = dQ/dt

The analogous definition of non linear inductance is

L(i) = dΦ/di.

In the operation of parametric devices, the mixing

effects occur when voltages at two or more different

frequencies are impressed on a nonlinear reactance.

dv

dQ

Derived a set of general energy relations regarding

power flowing into and out of an ideal nonlinear

reactance.

These relations are useful in predicting whether

power gain is possible in a parametric amplifier.

• One signal generator and one pump generator at their

respective frequencies , together with

associated series resistances and bandpass filters, are applied

to a nonlinear capacitance C(t).

• These resonating circuits of filters are designed to reject

power at all frequencies other than their respective signal

frequencies.

• In the presence of two applied frequencies

an infinite number of resonant frequencies of

are generated, where m and n are any integers.

Each of the resonating circuits is assumed to be

ideal.

The power loss by the nonlinear susceptance is

negligible. That is the power entering the nonlinear

capacitor at the pump frequency is equal to the

power leaving the capacitor at the other

frequencies through the nonlinear interaction.

Manley and Rowe established the power relations

between the input power at the frequencies

and the output power at the other frequencies

For Q to be real,

The total voltage v can be expressed as a function of

the charge Q.

A similar taylor series expression of v(Q) shows that

V to be real,

The current flowing through C(t) is the total

derivative of Q w r t time. Hence,

Where

Multiply the above equation by a factor of

and rearrangement of

the resultant into two parts yield

Since

Then,

Becomes,

And is independent of ωp or ωs.

For any choice of the frequencies fp and fs, the

resonating circuit external to thatof the nonlinear

capacitance C(t) can be so adjusted that the

currents may keep all the voltage amplitudes

Unchanged.

The charges are also unchanged, sincethey are

functions of the voltages.

Since , then

Similarly,

Where are replaced by

respectively.

The above equations are standard forms for the

Manley-Rowe power relations.

The term indicates the realpower flowing into

or leaving the nonlinear capacitor at a frequency of

.. The frequency represents the

fundamental frequency of the pumping voltage

oscillator and the frequency signifies the

fundamental frequency of the signal voltage

generator.