Electrically small, super directive antennas
An electrically small receiver system is provided. The receiver system includes a plurality of antennas and a signal processing circuit. The plurality of antennas includes a first antenna configured to receive a first signal and a second antenna configured to receive a second signal. The signal processing circuit includes a phase shifter configured to apply a phase shift to the received second signal. The phase shift applied by the phase shifter is a function of an angle of incidence of the second signal measured relative to a boresight direction of the plurality of antennas. The signal processing circuit is configured to form an output signal that is a combination of the received first signal and the phase shifted second signal.
1. A receiver system comprising:
a plurality of antennas comprising
a first antenna configured to receive a first signal; and
a second antenna configured to receive a second signal; and
a signal processing circuit comprising a phase shifter configured to apply a phase shift to the received second signal, wherein the phase shift applied by the phase shifter is a function of an angle of incidence of the second signal measured relative to a boresight direction of the plurality of antennas,
wherein the signal processing circuit is configured to form an output signal that includes the phase shifted second signal.
2. The receiver system of claim 1 , wherein the phase shifter is controlled by a phase difference determined between the received first signal and the received second signal.
3. The receiver system of claim 2 , further comprising:
a ninety degree phase shifter configured to receive the received first signal and to form a phase shifted first signal;
a first mixer configured to receive the received first signal and the received second signal and to form a first mixed signal;
a second mixer configured to receive the received second signal and the phase shifted first signal and to form a second mixed signal;
a first low pass filter configured to receive the first mixed signal and to form a first filtered signal;
a second low pass filter configured to receive the second mixed signal and to form a second filtered signal;
wherein the phase difference is determined based on the first filtered signal and the second filtered signal.
4. The receiver system of claim 3 , wherein the phase shift, Φ(θ), applied by the phase shifter is
Φ
(
θ
)
=
{
-
Φ
0
θ
<
θ
0
0
-
θ
0
<
θ
<
θ
0
Φ
0
θ
>
θ
0
,
where θ=sin −1 λδ/2πd is the angle of incidence, where δ is the determined phase difference, λ is the wavelength of the received second signal, d is the distance between the first antenna and the second antenna, θ 0 is half of a selected 3 dB beamwidth, and Φ 0 is defined such that an array factor, AF=1+e −j2πd sin(θ)/λ e −jφ 0 outside of the range −θ 0 <θ<θ 0 is minimum.
5. The receiver system of claim 4 , further comprising a summer configured to form the output signal as a sum of the received first signal and the phase shifted second signal.
6. The receiver system of claim 2 , wherein the phase shift, Φ(θ), applied by the phase shifter is
Φ
(
θ
)
=
{
-
Φ
0
θ
<
θ
0
0
-
θ
0
<
θ
<
θ
0
Φ
0
θ
>
θ
0
,
where θ=sin −1 λδ/2πd is the angle of incidence, where δ is the phase difference determined between the received first signal and the received second signal, λ is the wavelength of the received second signal, d is the distance between the first antenna and the second antenna, θ 0 is half of a selected 3 dB beamwidth, and Φ 0 is defined such that an array factor, AF=1+e −j2πd sin(θ)/λ e −jφ 0 outside of the range −θ 0 <θ<θ 0 is minimum.
7. The receiver system of claim 1 , wherein the phase shift, Φ(θ), applied by the phase shifter is Φ(θ)=m2πd sin θ/λ, where θ is the angle of incidence, λ is the wavelength of the received second signal, d is the distance between the first antenna and the second antenna, and m>1.
8. The receiver system of claim 1 , wherein the phase shift, Φ(θ), applied by the phase shifter is
Φ
(
θ
)
=
2
tan
-
1
(
θ
θ
3
d
B
)
-
2
π
d
sin
θ
/
λ
,
where θ is the angle of incidence, θ 3 dB is a selected 3 dB beamwidth, λ is the wavelength of the received second signal, and d is the distance between the first antenna and the second antenna.
9. The receiver system of claim 1 , wherein the phase shifter comprises a direct differential phase shifter.
10. The receiver system of claim 9 , wherein the direct differential phase shifter comprises:
a first microstrip line coupled to receive the received first signal and configured to form a first output signal that is a phase shifted version of the received first signal;
a second microstrip line coupled to receive the received second signal and configured to form the phase shifted second signal;
a nonlinear capacitor coupling the first microstrip line and the second microstrip line along their lengths; and
a summer configured to form the output signal as a sum of the first output signal and the phase shifted second signal.
11. The receiver system of claim 9 , wherein the direct differential phase shifter comprises:
a first amplifier coupled to receive the received first signal and configured to form a first amplified signal;
a first microstrip line coupled to receive the first amplified signal and configured to form a first output signal that is a phase shifted version of the first amplified signal;
a second amplifier coupled to receive the received second signal and configured to form a second amplified signal;
a second microstrip line coupled to receive the second amplified signal and configured to form the phase shifted second signal;
a nonlinear capacitor coupling the first microstrip line and the second microstrip line along their lengths; and
a summer configured to form the output signal as a sum of the first output signal and the phase shifted second signal.
12. The receiver system of claim 9 , wherein the direct differential phase shifter comprises:
a first down converter coupled to receive the received first signal and configured to form a first down converted signal at a lower frequency;
a first amplifier coupled to receive the first down converted signal and configured to form a first amplified signal;
a first microstrip line coupled to receive the first amplified signal and configured to form a first output signal that is a phase shifted version of the first amplified signal;
a second down converter coupled to receive the received second signal and configured to form a second down converted signal at the lower frequency;
a second amplifier coupled to receive the second down converted signal and configured to form a second amplified signal;
a second microstrip line coupled to receive the second amplified signal and configured to form the phase shifted second signal;
a nonlinear capacitor coupling the first microstrip line and the second microstrip line along their lengths; and
a summer configured to form the output signal as a sum of the first output signal and the phase shifted second signal.
13. The receiver system of claim 1 , wherein the phase shifter comprises:
a differential amplifier coupled to receive the received first signal and the received second signal and configured to form an amplified differential signal;
an amplitude detector coupled to receive the amplified differential signal and configured to rectify the amplified differential signal and to convert the rectified differential signal to DC to form a DC signal; and
a voltage controlled phase shifter coupled to receive the DC signal and the received second signal and configured to use the DC signal to control the phase shift applied to the received second signal to form the phase shifted second signal.
14. The receiver system of claim 13 , further comprising a summer configured to form the output signal as a sum of the received first signal and the phase shifted second signal.
15. The receiver system of claim 1 , wherein the phase shifter comprises a digital filter configured to provide a phase difference, Φ(θ)=m2πd sin θ/λ between a first digital version of the received first signal and a second digital version of the received second signal, where θ is the angle of incidence, λ is the wavelength of the received second signal, d is the distance between the first antenna and the second antenna, and m>1.
16. The receiver system of claim 1 , wherein the phase shifter comprises a digital filter configured to provide a phase difference,
Φ
(
θ
)
=
2
tan
-
1
(
θ
θ
3
d
B
)
-
2
π
d
sin
θ
/
λ
between a first digital version of the received first signal and a second digital version of the received second signal, where θ is the angle of incidence, θ 3 dB is a selected 3 dB beamwidth, λ is the wavelength of the received second signal, and d is the distance between the first antenna and the second antenna.
17. The receiver system of claim 1 , wherein the signal processing circuit further comprises:
a first analog-to-digital converter (ADC) coupled to receive the received first signal and configured to form a first digital signal;
a second ADC coupled to receive the received second signal and configured to form a second digital signal; and
a digital filter configured to provide a phase difference,
Φ
(
θ
)
=
2
tan
-
1
(
θ
θ
3
d
B
)
-
2
π
d
sin
θ
/
λ
,
between the first digital signal and the second digital signal to form a first filtered signal and the phase shifted second signal, where θ is the angle of incidence, θ 3 dB is a selected 3 dB beamwidth, λ is the wavelength of the received second signal, and d is the distance between the first antenna and the second antenna.
18. The receiver system of claim 17 , further comprising a summer configured to form the output signal as a sum of the first filtered signal and the phase shifted second signal.
19. The receiver system of claim 1 , wherein signal processing circuit further comprises:
a first down converter coupled to receive the received first signal and configured to form a first down converted signal at a lower frequency;
a first analog-to-digital converter (ADC) coupled to receive the first down converted signal and configured to form a first digital signal;
a second down converter coupled to receive the received second signal and configured to form a second down converted signal at the lower frequency;
a second ADC coupled to receive the second down converted signal and configured to form a second digital signal; and
a digital filter configured to provide a phase difference,
Φ
(
θ
)
=
2
tan
-
1
(
θ
θ
3
d
B
)
-
2
π
d
sin
θ
/
λ
,
between the first digital signal and the second digital signal to form a first filtered signal and the phase shifted second signal, where θ is the angle of incidence, θ 3 dB is a selected 3 dB beamwidth, λ is the wavelength of the received second signal, and d is the distance between the first antenna and the second antenna.
20. The receiver system of claim 1 , wherein the signal processing circuit further comprises:
a first analog-to-digital converter (ADC) coupled to receive the received first signal and configured to form a first digital signal;
a second ADC coupled to receive the received second signal and configured to form a second digital signal; and
a digital filter configured to provide a phase difference, Φ(θ)=m2πd sin θ/λ, between the first digital signal and the second digital signal to form a first filtered signal and the phase shifted second signal, where θ is the angle of incidence, λ is the wavelength of the received second signal, d is the distance between the first antenna and the second antenna, and m>1.