186
10 Multi-channel Radar Systems
The signals from two antennas are fed simultaneously to high-frequency sum
and equilibrium devices, which represent the waveguide bridges and performing
integration and subtract of signals directly at a high frequency:
U + = k
F(ϕ 0 + γ ) + F(ϕ 0 − γ )
sinωt,
U − = k
F(ϕ 0 + γ ) − F(ϕ 0 − γ )
sinωt.
(10.5)
After conversion and amplification of signals in the IF amplifier
´
U + = k
F(ϕ 0 + γ ) + F(ϕ 0 − γ )
sin(ω 0 t + ψ 1 ),
´
U − = k
F(ϕ 0 + γ ) − F(ϕ 0 − γ )
sin(ω 0 t + ψ 2 ).
(10.6)
where ψ 1 and ψ 2 —are phase shifts in channels.
The phase detector, to which the voltage of the sum channel is supplied as a
reference, and the voltage of the difference channel as a signal, performs voltage
multiplication. In this case, the phase detector filter removes high-frequency combinational components, and the voltage of the difference frequency is released at the
output:
U out = k pd
k 1 k 2
2
F
2
(ϕ 0 + γ ) − F
2
(ϕ 0 − γ )
cos(ψ 1 − ψ 2 )
(10.7)
Expansion of the functions F(ϕ) in a Taylor series near the point ϕ = ϕ 0 gives:
F(ϕ 0 + γ ) = F(ϕ 0 ) + γ
d F(ϕ)
dϕ
| ϕ=ϕ 0 + . . . ,
F(ϕ 0 − γ ) = F(ϕ 0 ) − γ
d F(ϕ)
dϕ
| ϕ=ϕ 0 + . . . .
(10.8)
Restricting ourselves to two terms of the series due to the small mismatch of γ,
we have the following:
U out = 2k pd k 1 k 2 F(ϕ 0 )γ
dF(ϕ)
dϕ
| ϕ=ϕ 0 cos(ϕ 1 − ϕ 2 )
(10.9)
In contrast to the direction-finding (boresight) characteristic of the amplitudedifference radar, the direction-finding characteristic of the amplitude summeddifference radar has a boresight direction that does not depend on the amplitude
and phase characteristics of the channels. This means that, despite the non-identity
of the channels (k 1 = k 2 ; ϕ 1 = ϕ 2 ), in the absence of mismatch (γ = 0), the output
voltage always turns to zero. An additional summary channel eliminates the target
bearing error. Both the non-identity of the channels and the amplitude fluctuations
of reflected signal lead to a change in the slope of the resulting direction-finding
characteristic (10.9), but do not influence on stability of the zero boresight.
10 Multi-channel Radar Systems
The signals from two antennas are fed simultaneously to high-frequency sum
and equilibrium devices, which represent the waveguide bridges and performing
integration and subtract of signals directly at a high frequency:
U + = k
F(ϕ 0 + γ ) + F(ϕ 0 − γ )
sinωt,
U − = k
F(ϕ 0 + γ ) − F(ϕ 0 − γ )
sinωt.
(10.5)
After conversion and amplification of signals in the IF amplifier
´
U + = k
F(ϕ 0 + γ ) + F(ϕ 0 − γ )
sin(ω 0 t + ψ 1 ),
´
U − = k
F(ϕ 0 + γ ) − F(ϕ 0 − γ )
sin(ω 0 t + ψ 2 ).
(10.6)
where ψ 1 and ψ 2 —are phase shifts in channels.
The phase detector, to which the voltage of the sum channel is supplied as a
reference, and the voltage of the difference channel as a signal, performs voltage
multiplication. In this case, the phase detector filter removes high-frequency combinational components, and the voltage of the difference frequency is released at the
output:
U out = k pd
k 1 k 2
2
F
2
(ϕ 0 + γ ) − F
2
(ϕ 0 − γ )
cos(ψ 1 − ψ 2 )
(10.7)
Expansion of the functions F(ϕ) in a Taylor series near the point ϕ = ϕ 0 gives:
F(ϕ 0 + γ ) = F(ϕ 0 ) + γ
d F(ϕ)
dϕ
| ϕ=ϕ 0 + . . . ,
F(ϕ 0 − γ ) = F(ϕ 0 ) − γ
d F(ϕ)
dϕ
| ϕ=ϕ 0 + . . . .
(10.8)
Restricting ourselves to two terms of the series due to the small mismatch of γ,
we have the following:
U out = 2k pd k 1 k 2 F(ϕ 0 )γ
dF(ϕ)
dϕ
| ϕ=ϕ 0 cos(ϕ 1 − ϕ 2 )
(10.9)
In contrast to the direction-finding (boresight) characteristic of the amplitudedifference radar, the direction-finding characteristic of the amplitude summeddifference radar has a boresight direction that does not depend on the amplitude
and phase characteristics of the channels. This means that, despite the non-identity
of the channels (k 1 = k 2 ; ϕ 1 = ϕ 2 ), in the absence of mismatch (γ = 0), the output
voltage always turns to zero. An additional summary channel eliminates the target
bearing error. Both the non-identity of the channels and the amplitude fluctuations
of reflected signal lead to a change in the slope of the resulting direction-finding
characteristic (10.9), but do not influence on stability of the zero boresight.