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# RF Electronics & Analysing the Magnetron Drive Circuit

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This solution deals with the analysis of a given Magnetron Drive Circuit to derive the circuit characteristics as applied to a resulting Radar pulse. Circuit parameters are given including Delay Line parameters and from this such things as the number of turns on the secondary winding of the drive transformer, the pulse period and duration, DC input power requirements and outgoing RF pulse power are derived.

https://brainmass.com/physics/circuits/rf-electronics-analysing-magnetron-drive-circuit-344802

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Determination of circuit parameters for a Magnetron Drive Circuit - RF Electronics

PROBLEM:

A Magnetron Drive Circuit is described by the circuit shown in Figure 1. In addition the said Magnetron has the following circuit parameters defined.

Magnetron Definition parameters:

Input impedance of Magnetron (ZMAG ) = 625 Ohms
DC to RF conversion efficiency of Magnetron (Eff (DC-RF) ) = 75 % = 0.75

Magnetron Drive circuitry definition:

{SEE ATTACHMENT FOR CIRCUIT DIAGRAM}

VS = 1 kV, LCH = 3.12 H, L = 160 nH, C = 260 pF, no. sections in LC delay
line n = 20

Figure 1: A Magnetron Drive Circuit

(Q1) Determine an estimate for the required number of turns (N) on the secondary of
the transformer.

(A1) Theory states that the output impedance as seen by the transformer (in this case
the input impedance of the Magnetron) is given as the input impedance (in this
case the delay line impedance) multiplied by the transformer turns ratio squared.

Equation  shows this general identity

N2/n2 = ZMAG / Z0 

{where N represent the turns on the secondary winding, n represents the turns on the primary transformer winding}.

Since in this case the primary winding is just represented as one turn, n = 1, we can simplify  to  as below.

N2 = ZMAG / Z0 

Also from standard theory we can say that the characteristic delay line impedance, Z0 , can be calculated from the identity involving the square root of the Inductance to Capacitance ratio shown in 

Z0 = Sqrt(L/C) 

 substituted into  and square rooted yields  as

N = (ZMAG)^1/2*(C/L)^1/4 

Putting values given into  yields an estimate for number of turns required on the secondary winding of the transformer, thus

N = (625)^1/2*(260 x 10-12 / 160 x 10-9)^1/4 turns

N ~ 5 turns

(Q2) Estimate the amplitude (VP) of the resulting Radar voltage pulse

(A2) The voltage VS is applied as a discharge to the input of transformer

The pulse amplitude (VP ) to the Magnetron is simply this voltage multiplied by the turns ratio N and is given by  as

VP = N*VS 

Putting in values given or calculated yields an estimate for the amplitude of the Radar pulse of

VP = 5 x 1 kV = 5 kV

(Q3) Calculate the period (T) of the pulse applied to the Magnetron

(A3) The period of the pulse can be determined from standard theory and is given
by 

T = pi*Sqrt(LCH*nC) 

Substituting the values given into  an estimate for the pulse period can be made as

T = pi*Sqrt(3.12 x 20 x 260 x 10^-12 ) s

T = 400 us

(Q4) Determine an estimate for the duration (&#964;) of the pulse applied to the Magnetron

(A4) The duration (t) of the pulse applied to the Magnetron is defined by circuit theory
and is given by 

t = n*Sqrt(LC) 

Putting in values given to  we can estimate the pulse duration as

t = 20*Sqrt(160 x 10^-9 x 260 x 10^-12) s

t = 0.129 us

(Q5) Estimate the pulse power (PDC) given to the Magnetron

(A5) The DC pulse power is given by  via the classical Power = Voltage Squared x
Impedance.

As we are looking at the input side to the transformer then

PDC = (VS )2 Z0 

Where Z0 is given by  (Equation  transformed) as

Z0 = ZMAG / N2 

 in  yields  as

PDC = (VS )2 ZMAG / N2 

Putting in the values given in to  gives an estimate of the pulse power input to
the Magnetron as

PDC = (1000 )2 x 625 / 25 = 25 MW

(Q6) Find the RF power (PRF ) transmitted by the Magnetron.

(A6) The RF power transmitted by the Magnetron is given as the product of the power
conversion efficiency and the DC power calculated previously in (A5). It is
shown by the identity 

PRF = Eff(DC-RF) *PDC 

Putting in values given to  gives an estimate for the RF pulse power as

PRF = 0.75 x 25 = 18.75 MW

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