A Novel Integrated Power Module with Solid-State …
13
ζ = −
cos(ψ i − θ L )
sin(θ i − θ L )
ν =
cos(θ i − ψ L )
sin(ψ i − ψ L )
(12)
with k =
2π
λ r
, λ r is the resonant wavelength, h, r i , r L , and Z L are as shown in Fig. 9.
Considering the oscillation condition for IMPATT diode placed in a resonant-cap
cavity, i.e.: Z g + Z D = 0, where Z g = (h/2π r g )Z i, and Z D is given by: 1/ωC d ; Z i being
given by Eq. (9). At r g = r L we have after some manipulation the expression for Z L
as:
Z L =
2πr L
h
Z 0 (r L )η
2π Z 0 (r i )ζ f r C d − ζ
2
1 + 2π Z 0 (r i )ν f r C d
0.5
(13)
where C d is the diode capacitance and f r is the resonant frequency of the oscillator.
The computed results based on analytical model equations reported by Kar [11]
indicate the following about resonant-cap oscillator.
1. The load impedance (Z L ) at the terminating end of the cap cavity is very close
to the characteristic impedance of the waveguide in which the cap cavity with the
diode embedded in it resides. This indicates that the resonant-cap (with its radius
approximately a quarter wavelength) acts as quarter-wave impedance transformer
between the device impedance and the waveguide characteristic impedance ensuring
efficient operation of resonant-cap oscillator in terms of maximum possible power
transfer from the device to the load.
2. The cap diameter primarily responsible for determining the oscillation
frequency (f r ) of the cap-type oscillator though cap height also changes oscillation
frequency slightly. However, cap height is significantly responsible for influencing
the real part of the cap impedance at the device plane which is useful for oscillator
design as the oscillation condition demands that Re(R D ) ≥ R C . Tailoring of R C with
cap height will be an important design criterion of cap-type oscillator design.
4 Device-Circuit Interaction and Oscillator
Characterization
The oscillator characteristics can be evaluated in terms of the interaction of the
IMPATT device with the circuit (in this case the resonant-cap circuit whose analytical
model equations have been developed above). For IMPATT diode, large-signal model
equations will be used to derive the model equations for oscillator characterization
in terms of device-circuit interaction.
13
ζ = −
cos(ψ i − θ L )
sin(θ i − θ L )
ν =
cos(θ i − ψ L )
sin(ψ i − ψ L )
(12)
with k =
2π
λ r
, λ r is the resonant wavelength, h, r i , r L , and Z L are as shown in Fig. 9.
Considering the oscillation condition for IMPATT diode placed in a resonant-cap
cavity, i.e.: Z g + Z D = 0, where Z g = (h/2π r g )Z i, and Z D is given by: 1/ωC d ; Z i being
given by Eq. (9). At r g = r L we have after some manipulation the expression for Z L
as:
Z L =
2πr L
h
Z 0 (r L )η
2π Z 0 (r i )ζ f r C d − ζ
2
1 + 2π Z 0 (r i )ν f r C d
0.5
(13)
where C d is the diode capacitance and f r is the resonant frequency of the oscillator.
The computed results based on analytical model equations reported by Kar [11]
indicate the following about resonant-cap oscillator.
1. The load impedance (Z L ) at the terminating end of the cap cavity is very close
to the characteristic impedance of the waveguide in which the cap cavity with the
diode embedded in it resides. This indicates that the resonant-cap (with its radius
approximately a quarter wavelength) acts as quarter-wave impedance transformer
between the device impedance and the waveguide characteristic impedance ensuring
efficient operation of resonant-cap oscillator in terms of maximum possible power
transfer from the device to the load.
2. The cap diameter primarily responsible for determining the oscillation
frequency (f r ) of the cap-type oscillator though cap height also changes oscillation
frequency slightly. However, cap height is significantly responsible for influencing
the real part of the cap impedance at the device plane which is useful for oscillator
design as the oscillation condition demands that Re(R D ) ≥ R C . Tailoring of R C with
cap height will be an important design criterion of cap-type oscillator design.
4 Device-Circuit Interaction and Oscillator
Characterization
The oscillator characteristics can be evaluated in terms of the interaction of the
IMPATT device with the circuit (in this case the resonant-cap circuit whose analytical
model equations have been developed above). For IMPATT diode, large-signal model
equations will be used to derive the model equations for oscillator characterization
in terms of device-circuit interaction.