The S22from the schematic extraction is reasonable. But in measurement extraction results, from Figure2.22, the variation for S22 between the extracted results and the single-ended results gets bigger as frequency goes higher. The reason for this inaccuracy may be caused by having coupling to ground problems for the designed PCB or the choke inductors are not large enough to be considered as open circuit when in parallel with the ouput port with open termination in the simulations. Because the internal transmission lines has big influence to the extraction results, the layout has to be designed in the way that least internal transmission lines are used as shown in Figure2.16. The future work for this project would be to find a way of improving the algorithms to accommodate grounding and finite choke inductor problems, which are found in the circuit.
Ideal Differential Circuit
Noise Parameters Frequency Single-Ended(A/B) Extracted(A/B) Variation NFmin 500 MHz 1.023 dB/1.052 dB 1.023 dB/1.052 dB 0 dB/0 dB 1.5 GHz 1.047 dB/1.102 dB 1.047 dB/1.102 dB 0 dB/0 dB
Rn 500 MHz 11Ω/14.5Ω 11Ω/14.5Ω 0Ω/0Ω
1.5 GHz 11Ω/13Ω 11Ω/13Ω 0Ω/0Ω
Γopt 500 MHz 0.905 + j0.095/0.838 + j0.059 0.905 + j0.095/0.838 + j0.059 0/0 1.5 GHz 0.715 + j0.380/0.594 + j0.371 0.715 + j0.380/0.594 + j0.371 0/0 Table 4.3: Comparison of Ideal Differential-Circuit Extraction Results with Single-Ended Simulation Results.
45
Schematic
Noise Parameters Frequency Single-Ended Extracted Variation
NFmin 502.5 MHz 2.38 dB 1.71 dB 0.67 dB
1.515 GHz 2.36 dB 1.74 dB 0.62 dB
Rn 502.5 MHz 21.28Ω 20.29Ω 0.99Ω
1.515 GHz 20.39Ω 21.01Ω −0.62Ω
Γopt 502.5 MHz 0.220 + j0.056 0.209 + j0.055 -1.515 GHz 0.202 + j0.072 0.207 + j0.076
-Table 4.4: Comparison of NFmin, Rn, and Γopt Obtained from Schematic Simulations to the Relevant Single-Ended Simulation Results .
Measurement Amplifier A Measurement Amplifier B S12 502.5 MHz −19.176 dB −23.372 dB 4.196 dB −19.176 dB −22.488 dB 3.312 dB 1.515 GHz −13.299 dB −17.289 dB 3.99 dB −13.299 dB −16.529 dB 3.23 dB S21 502.5 MHz 8.067 dB 8.451 dB −1.017 dB 8.067 dB 9.084 dB −0.633 dB
1.515 GHz 4.272 dB 5.023 dB −0.751 dB 4.272 dB 4.575 dB −0.303 dB S22 502.5 MHz −6.639 dB −4.229 dB −2.41 dB −6.639 dB −4.594 dB −2.045 dB 1.515 GHz −6.185 dB −1.060 dB −5.125 dB −6.185 dB −0.943 dB −5.242 dB
Directly
Table 4.5: Comparison of S-Parameters from Measurement Results to the Relevant Ended Measurement Results for Single-Ended Amplifiers and the Common Network Impedance
47
Measurement Amplifier A (after smooth function) Measurement Amplifier B (after smooth function) Noise Parameters Frequency Single-Ended Extracted Variation Single-Ended Extracted Variation
NFmin 502.5 MHz 2.05 dB 1.84 dB 0.21 dB 2.05 dB 2.04 dB 0.01 dB
1.515 GHz 2.10 dB 1.97 dB 0.13 dB 2.10 dB 2.14 dB −0.04 dB
Rn 502.5 MHz 38.73Ω 23.55Ω 15.18Ω 38.73Ω 45.71Ω −6.98Ω
1.515 GHz 25.89Ω 21.44Ω 4.45Ω 25.89Ω 27.56Ω −1.67Ω
Γopt 502.5 MHz 0.350 + j0.016 0.226 + j0.086 - 0.350 + j0.016 0.444 + j0.136 -1.515 GHz 0.125 − j0.033 0.066 + j0.164 - 0.125 − j0.033 0.108 + j0.185 -Table 4.6: Comparison of NFmin, Rn, andΓopt Obtained from Measurements to the Relevant Single-Ended Measurement Results.
48
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Appendix A
Forming Matrix to Solve S-Parameters for Single Amplifier Inside a Differential Amplifier
To form the matrix mentioned in (2.4) with the purpose of finding the 2-port S-parameters for the terminated differential Ampplifier B (which means Port 2 and Port 4 are terminated) as mentioned in Section 2.2. Firstly, the 4-port S parameters can be represented in the following way
where Vi+are the wave amplitudes entering Port i, Vj−are the wave amplitudes exiting Port j,
Similar transforms can be applied to other similar terms, so (A.6) can be represented in the way as shown in (A.8)
S11′ = S11+ S12
With (A.8), (A.9), and (A.10), the following matrix that was used in (2.4) can be formed (when calculating S11 of a two port, V2+ which represents the wave going into Port 2 will set to be 0):
represents the input reflection coefficient when looking from the termi-nated input port of Amplifier B into the load, Γ4 = VV4+−
4
represents the output reflection coefficient when looking from the terminated output port of Amplifier B into the load, S′i j=Vi+
Vj−|V+
k =0 f or k6= jrepresenting the 2-port S parameters for the differential amplifier with one side terminated. This matrix can be solved to find S′11.
Similarly, to find S′22, it needs to divide both sides of the (A.3), (A.4) and (A.5) by V3+. Similarly, this time V1+= 0. The following matrixes are found
The above procedures are designed to find the overall 2-port S parameters (S′a) measured from the input and output ports of Amplifier A with Amplifier B terminated as shown in Figure (2.3). If measuring Amplifier B with Amplifier A terminated, by following the above steps, S′bcan be found. Γ2andΓ4are the two variables, which would change according to different load situations.
Appendix B