Model XC0450A-03
Rev B
Reflections From Equal Unmatched Terminations
Referring to the illustration below, consider the following reflection properties of the 3dB coupler. A signal applied to
port 1 is split and appears at the two output ports, ports 3 & 4, with equal amplitude and in phase quadrature. If ports
3 & 4 are not perfectly matched to 50ꢀ there will be some signal reflected back into the coupler. If the magnitude and
angle of these reflections are equal, there will be two signals that are equal in amplitude and in phase quadrature (i.e.
the reflected signals) being applied to ports 3 & 4 as inputs. These reflected signals will combine at the isolated port
and will cancel at the input port. So, terminations with the same mismatch placed at the outputs of the 3dB coupler will
not reflect back to the input port and therefore will not affect input return loss.
Γ× 0.707V ∠θ
0.707V∠θ (-3dB)
Γ (0.5V ∠2θ + 0.5V ∠2θ -180) = 0V
4
Termination = ZL
1V
1
Z
L
L
− Z
+ Z
0
0
Γ=
Z
Isolated Port
2
Termination = ZL
3
0.707V ∠θ -90 (-3dB)
Γ× 0.707V ∠θ -90
|Γ (0.5V ∠2θ -90 + 0.5V ∠2θ -90)| = |Γ|
The reflection property of common mismatches in 3dB couplers is very beneficial to the operation of many networks.
For instance, when splitter/combiner networks are employed to increase output power by paralleling transistors with
similar reflection coefficients, input return loss is not degraded by the match of the transistor circuit. The reflections
from the transistor circuits are directed away from the input to the termination at the isolated port of the coupler.
This example is not limited to Power Amplifiers. In the case of Low Noise Amplifiers (LNA’s), the reflection property of
3dB couplers is again beneficial. The transistor devices used in LNA’s will present different reflection coefficients
depending on the bias level. The bias level that yields the best noise performance does not also provide the best
match to 50 ꢀ. A circuit that is optimized for both noise performance and return loss can be achieved by combining
two matched LNA transistor devices using 3dB couplers. The devices can be biased for the best noise performance
and the reflection property of the couplers will provide a good match as described above. An example of this circuit is
illustrated below:
LNA Circuit Leveraging the Reflection Property of 3dB Couplers
50Ω
Termination
Input
50Ω
Termination
Output
Amplitude and phase tracking
Energy reflected from LNA
LNA devices biased for
optimum noise performance
devices biased for optimum
noise performance
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