Dynamic real-time calibration for antenna matching in a radio frequency receiver system
This disclosure relates to real-time calibration of a tunable matching network that matches the dynamic impedance of an antenna in a radio frequency receiver system. The radio frequency receiver system includes two non-linear equations that may be solved to determine the reflection coefficient of the antenna. Control system that calculates, in real time, a value of an input impedance of the antenna to match a load in a receiver system, wherein said impedance is calculated directly using a closed-form solution. The reflection coefficient of the antenna may be used to determine the input impedance of the antenna. The elements of the matching circuit are then adjusted to match the input impedance of the antenna.
1. A method of matching the input impedance of an antenna to a load of a receiver in a wireless communications system, comprising:
using a control system to calculate, in real-time, a value of an input impedance Z A of the antenna to match a load impedance Z 0 in a receiver system, wherein said input impedance Z A of the antenna is calculated directly using closed-form solution formulas, the closed-form solution formula inputing three power values measured when reactive elements of a matching network are perturbed and resultant power values, P L (1) , P L (2) , and P L (3) corresponding to each perturbation are recorded, the three power values being used in an intermediate calculation of real and imaginary components of a reflection coefficient Γ A of the antenna to calculate the input impedance Z A from the relationship
Z
A
=
1
+
Re
(
Γ
A
)
+
j
Im
(
Γ
A
)
1
-
Re
(
Γ
A
)
-
j
Im
(
Γ
A
)
Z
0
;
using a digital-to-analog converter to convert the input impedance of the antenna to a number of voltage values that tune the matching network; and
tuning, using the number of voltage values, the matching network to match the calculated values of the input impedance of the antenna to the load on the receiver system, P L (1) P L (2) P L (3) .
2. The method of claim 1 , wherein the control system receives a reference received power value, a first received power value, and a second received power value to determine a reflection coefficient of the antenna.
3. The method of claim 2 , wherein the reference received power value, first received power value, and second received power value are measured at a specific node of the matching network.
4. The method of claim 3 , wherein the first received power value is the power measured of the receiver system after a first perturbation of a number of reactive elements in the matching network.
5. The method of claim 3 , wherein the second received power value is the power measured from the receiver system after a second perturbation of a number of reactive elements in the matching network, wherein the first perturbation is different from the second perturbation.
6. The method of claim 3 , wherein the control system converts the determined reflection coefficient of the antenna to the input impedance of the antenna.
7. The method of claim 1 , wherein the control system calculates the value of the input impedance of the antenna by solving two non-linear equations.
8. The method of claim 7 , a first non-linear equation of the two non-linear equations is expressed as:
P
L
(
1
)
P
L
(
0
)
=
S
22
(
1
)
2
1
-
S
22
(
0
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
0
)
2
S
21
(
0
)
2
1
-
S
22
(
1
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
1
)
2
,
wherein
P
L
(
1
)
P
L
(
0
)
is the ratio of power received by the load at a first tuning position of the reactive elements of the matching network; S 22 (1) is a scattering matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input after a first perturbation of the matching network; S 22 (0) is a matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input in a previous tuning period; S 21 (0) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output in a previous tuning period; Γ L is a reflection coefficient of the load, and Γ in (0) is an input reflection coefficient of the matching network as seen from the antenna in a previous tuning period; Γ in (1) is an input reflection coefficient of the matching network as seen from the antenna after a first perturbation of the matching network; and Γ A is the reflection coefficient of the antenna.
9. The method of claim 7 , wherein a second non-linear equation of the two non-linear equations is expressed as:
P
L
(
2
)
P
L
(
0
)
=
S
21
(
2
)
2
1
-
S
22
(
0
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
0
)
2
S
21
(
0
)
2
1
-
S
22
(
2
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
2
)
2
,
wherein
P
L
2
P
L
(
0
)
is the ratio of power received by the load at a second tuning position of the reactive elements of the matching network; S 22 (2) is a scattering matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input after a second perturbation of the matching network; S 22 (0) is a matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input in a previous tuning period; S 21 (0) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output in a previous tuning period; S 21 (2) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output after a second perturbation of the matching network; Γ L is a reflection coefficient of the load, and Γ in (0) is an input reflection coefficient of the matching network as seen from the antenna in a previous tuning period; Γ in (2) is an input reflection coefficient of the matching network as seen from the antenna after a second perturbation of the matching network; and Γ A is the reflection coefficient of the antenna.
10. A wireless communications system, comprising:
an antenna;
a control system that calculates, in real-time, a value of an input impedance Z A of the antenna to match a load impedance Z 0 in a receiver system, wherein said input impedance Z A of the antenna is calculated directly using closed-form solution formulas, the closed-form solution formula inputing three power values measured when reactive elements of a matching network are perturbed and resultant power values, P L (1) , P L (2) , and P L (3) corresponding to each perturbation are recorded, the three power values being used in an intermediate calculation of real and imaginary components of a reflection coefficient Γ A of the antenna to calculate the input impedance Z A from the relationship
Z
A
=
1
+
Re
(
Γ
A
)
+
j
Im
(
Γ
A
)
1
-
Re
(
Γ
A
)
-
j
Im
(
Γ
A
)
Z
0
;
a digital-to-analog converter that converts the input impedance of the antenna to a number of voltage values that tune the matching network; and
the matching network that is tuned using the number of voltage values to match the calculated values of the input impedance Z A of the antenna to the load impedance Z 0 on the receiver system P L (1) P L (2) P L (3) .
11. The wireless communications system of claim 10 , wherein the receives a reference received power value, a first received power value, and a second received power value to determine a reflection coefficient of the antenna.
12. The wireless communications system of claim 11 , wherein the reference received power value, first received power value, and second received power value are measured at a specific node of the matching network.
13. The wireless communications system of claim 12 , wherein the first received power value is the power measured of the receiver system after a first perturbation of a number of reactive elements in the matching network.
14. The wireless communications system of claim 12 , wherein the second received power value is the power measured from the receiver system after a second perturbation of a number of reactive elements in the matching network, wherein the first perturbation is different from the second perturbation.
15. The wireless communications system of claim 12 , wherein the control system converts the determined reflection coefficient of the antenna to the input impedance of the antenna.
16. The wireless communications system of claim 10 , wherein the control system calculates the value of the input impedance of the antenna by solving two non-linear equations.
17. The wireless communications system of claim 16 , a first non-linear equation of the two non-linear equations is expressed as:
P
L
(
1
)
P
L
(
0
)
=
S
22
(
1
)
2
1
-
S
22
(
0
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
0
)
2
S
21
(
0
)
2
1
-
S
22
(
1
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
1
)
2
,
wherein
P
L
(
1
)
P
L
(
0
)
is the ratio of power received by the load at a first tuning position of the reactive elements of the matching network; S 22 (1) is a scattering matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input after a first perturbation of the matching network; S 22 (0) is a matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input in a previous tuning period; S 21 (0) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output in a previous tuning period; Γ L is a reflection coefficient of the load, and Γ in (0) is an input reflection coefficient of the matching network as seen from the antenna in a previous tuning period; Γ in (1) is an input reflection coefficient of the matching network as seen from the antenna after a first perturbation of the matching network; and Γ A is the reflection coefficient of the antenna.
18. The wireless communications system of claim 16 , wherein a second non-linear equation of the two non-linear equations is expressed as:
P
L
(
2
)
P
L
(
0
)
=
S
21
(
2
)
2
1
-
S
22
(
0
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
0
)
2
S
21
(
0
)
2
1
-
S
22
(
2
)
Γ
L
2
1
-
Γ
A
Γ
i
n
(
2
)
2
,
wherein
P
L
2
P
L
(
0
)
is the ratio of power received by the load at a second tuning position of the reactive elements of the matching network; S 22 (2) is a scattering matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input after a second perturbation of the matching network; S 22 (0) is a matrix parameter that represents an output reflection coefficient of a 50 ohm terminated input in a previous tuning period; S 21 (0) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output in a previous tuning period; S 21 (2) is a scattering matrix parameter which represents the forward transmission coefficient of a 50 ohm terminated output after a second perturbation of the matching network; Γ L is a reflection coefficient of the load, and Γ in (0) is an input reflection coefficient of the matching network as seen from the antenna in a previous tuning period; Γ in (2) is an input reflection coefficient of the matching network as seen from the antenna after a second perturbation of the matching network; and Γ A is the reflection coefficient of the antenna.