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[<< Home](/home#4-signal-transport-panel-charges-3-and-4)
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[<< Section 4.3](./4.3)
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## 4.4 Link Performance
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The single-channel TX and RX boards have been tested jointly in order to characterize the performance of the full RFoF link. The ganged SMP connector, T-line, and Bias-T before the first amplifier on the transmitter that are required in the production RFoF link are not on the single-channel TX board, and were consequently not part of these tests. The test configurations and results are explained below.
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### System Gain
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A Vector Network Analyzer (VNA) was used to find the S-Parameters of the single-channel RFoF link, which included a single-channel TX board connected to a single-channel RX board via one optical fiber adapter. The 16-channel balun board and Xilinx ZCU216 were not included. A separate test was performed using the RFSoC of the Xilinx ZCU216 to find the full signal transport link gain including the loss through the 16-channel balun board and 4 fiber connectors between the single-channel TX and RX boards. The variable attenuators on the TX board and RFSoC were set to 0 dB for these measurements (see Fig. 1).
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<div align="center">
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<img src="../uploads/32e83cbad608b43fbef8828b8b95d4f2/tx_r3-3_s21_alone.png" width="470"/>
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<img src="../uploads/095dad79176c547dcded08114bf61a1c/TX_r3-3_4fiber_RX1_rev2_RFSoC_gain.png" width="470"/>
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Figure 1: Top: Channel gain, or S21, of the system as measured on the VNA, Bottom: Full RFoF system gain measured on the RFSoC.
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</div>
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### Noise Temperature
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The RFoF equivalent noise temperature ($`T_{eq}`$) was calculated using the Y-factor method and an Equivalent Noise Ratio (ENR) source. Data was captured on the RFSoC of the Xilinx ZCU216, with the single-channel RX and 16-channel balun board used together as the receiver system. Since there will be up to 4 optical fiber connections between the two RFoF sub-systems at GBO, 4 fiber connections were in place between TX and RX boards during these tests.
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With natural gain variability in a multichannel phased array receiver, signal leveling is critical. Attenuators are included to ensure that signal levels are optimal for RFoF dynamic range and ADC sampling range. As the laser has the lowest 1 dB gain compression point (P1dB) and introduces the most noise to the link, attenuating before the laser increases the dynamic range of the system but also increases the noise. We want the widest range possible between the noise floor and gain compression, while contributing less than 1K to the total system noise temperature in our operational band. Figure 2 shows the RFoF equivalent noise temperature with different variable attenuator settings.
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Note that though the RFoF link noise temperature, $`T_{\rm eq}`$, is in the range of several hundreds of degrees Kelvin, due to very low noise temperature at the first cryo-cooled LNA, with significant gain preceding the RFoF link, all curves in the plot below the dashed light blue line will lead to a link noise contribution of less than $`1 K`$ in the target of $`T_{\rm sysq} = 26 K`$.
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<div align="center">
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<img src="../uploads/b5218d791f795dea6d96a406837c05cf/TX_r3-3_4fiber_RX1_rev2_RFSoC_T_eq_845Klim.png" width="600"/>
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Figure 2: Equivalent noise temperature of the RFoF through RFSoC system with different attenuator settings on the TX board.
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</div>
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Assuming a constant cryo-LNA gain of 35 dB, it is estimated that the signal transport contributes 1K to $`T_{sys}`$ when the equivalent noise temperature of the RFoF thru RFSoC link reaches 845K (dashed line). We can attenuate up to 15 dB before $`T_{eq}`$ passes this limit at the ALPACA band edges, and up to 17 dB before it passes the limit at the upper edge of our digital band (1662.5 MHz).
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We also want to bring the output P1dB of the RFoF link down to the full-scale power of the RFSoC ADCs, and be able to do gain leveling across all channels. This requires the use of the digital step attenuator (DSA) on the RFSoC. The RFSoC has a noise figure of about 25 dB, so increasing this attenuation on the RFSoC increases the system noise significantly (see Fig. 3).
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<div align="center">
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<img src="../uploads/8f6031d4de2d3ee499663e2a8b55fa0c/TX_r3-3_4fiber_RX1_rev2_RFSoC_atten_T_eq_845Klim.png" width="600"/>
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Figure 3: Equivalent noise temperature of the RFoF through RFSoC system with different attenuator settings on the TX board and the digital step attenuator on the RFSoC.
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</div>
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With 5 dB of attenuation on the RFSoC's DSA, the output P1dB of the RFoF link reaches a maximum at the ADC's full-scale power level of 1 dBm (see the following section). With this attenuation on the DSA, we can set the variable attenuator on the TX up to 10 dB before $`T_{eq}`$ reaches 845K at the upper operational band edge. Operating under this condition will maximize dynamic range while still meeting the target noise budget.
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The modelled overall system noise temperature for ALPACA, using measured cryo-LNA gain and assuming 16 K of noise from the antenna elements, is shown in Figure 4. The noise contribution of the RFoF thru RFSoC system is shown for multiple attenuator settings. No attenuation implies 0 dB of attenuation on the TX board and RFSoC, mid attenuation corresponds to 11 dB of attenuation on the TX board, and high attenuation corresponds to 10.5 dB of attenuation on the TX and 5 dB of attenuation on the RFSoC.
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<div align="center">
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<img src="../uploads/af3054871b79f3e6ffec0b3fd264638f/ALPACA_Tsys_mult_atten.png" width="600"/>
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Figure 4: ALPACA system noise temperature using approximate Tsys model for system prior to the RFoF link.
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</div>
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### Dynamic Range
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The 1 dB compression point measurements were made using data capture on the RFSoC of the Xilinx ZCU216, with the single-channel receiver and 16-channel balun board used together as the receiver sub-system. For this test, a single-frequency tone from a signal generator was set at 200 evenly spaced frequencies between 1250 and 1750 MHz. At each frequency, the tone power was increased incrementally from about -55 dBm until the system reached compression. The output P1dB can then be determined by adding the system gain (in dB) to the input P1dB. Figure 5 shows the input and output P1dB of the single-channel RFoF system for two attenuator settings, 0 dB and 10 dB. Note that the output P1dB was insensitive to this attenuator change.
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<div align="center">
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<img src="../uploads/7b44e53836901c93ecb392c01a666642/TX_r3-3_4fiber_RX1_rev2_RFSoC_P1dB_plot.png" width="470"/>
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<img src="../uploads/d5123ffe9f40d54b395b25b58f09793b/TX_r3-3_10dB_atten_4fiber_RX1_rev2_RFSoC_P1dB_plot.png" width="470"/>
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Figure 5: Input and output P1dB of the RFoF system. Top: TX attenuator set to 0 dB, Bottom: TX attenuator set to 10 dB.
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</div>
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Third-order intercept point (IP3) measurements for the full link have not been performed on our most recent single-channel RFoF system, but the output IP3 is estimated to be about 12 dBm across our band.
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Linear dynamic range (LDR) is defined as the difference between P1dB and the minimum detectable signal (in dB). For our system, this can be found by taking the difference between the output P1dB and the noise floor (see Fig. 6).
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<div align="center">
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<img src="../uploads/1213d60292fda307db9f4e6b1162dea7/TX_r3-3_4fiber_RX1_rev2_RFSoC_LDR_845Klim_10dB_atten.png" width="600"/>
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Figure 6: Linear dynamic range of the RFoF system for two attenuator settings. The blue curve uses 0 dB attenuation for both TX and RX, and corresponds to our highest ling gain setting. The orange curve uses 10 dB attenuation on TX and 5 dB on RX, which was shown experimentally above to yield highest dynamic range for the cases tested.
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</div>
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Spurious-free dynamic range (SFDR) is defined as the difference between P1dB and the minimum detectable spur (in dB). Since the highest spurs in our system are third-order intermodulation products, the SFDR can be calculated using the equation, $`SFDR = {\frac 2 3}*(OIP3 - P_{noise})`$, where $`OIP3`$ is the output third-order intercept point in dBm, and $`P_{noise}`$ is the system noise power. Figure 7 shows the estimated SFDR of the RFoF system.
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<div align="center">
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<img src="../uploads/d26840277153a3a180b4586ee326be87/TX_r3-3_4fiber_RX1_rev2_RFSoC_estimated_SFDR_845Klim_10dB_atten.png" width="600"/>
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Figure 7: Estimate spurious-free dynamic range of the RFoF system, using 12 dBm as the output third-order intercept point. Again, the orange curve uses 10 dB attenuation on TX and 5 dB on RX, which was shown experimentally above to yield highest dynamic range for the cases tested.
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</div>
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### Summary
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The ALPACA RFoF signal transport system has been tested using the single-channel TX and RX boards in conjunction with the 16-channel balun board and the RFSoC on the Xilinx ZCU216 on the receive end, and the results shown above represent the performance of the final system. Table 1 gives a summary of the performance specifications within our operational band.
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Table 1: Recommended attenuator settings and corresponding performance specifications of the ALPACA signal transport system
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| Parameter \ Condition | Performance target: <br> Maximize Dynamic Range | Performance target: <br> Minimize Noise |
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| ------: | ------ | ------|
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| TX Attenuation | 10 dB | 0 dB |
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| RFSoC DSA Setting | 5 dB | 0 dB |
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| Average Gain | 27 dB | 42 dB |
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| Link only $`T_{eq}`$ | 845 K | 170 K |
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| LDR [^1-LDRdB] | 142 dB*Hz | 128 dB*Hz |
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| SFDR [^2-SFDRdB] | 102 dB*Hz^(2/3) | 94 dB*Hz^(2/3) |
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[Section 5.1 >>](/5-dbe/5.1)
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## Footnotes
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[^1-LDRdB]: LDR specified in units of dB*Hz. Put in units of dB by subtracting 86 dB, which is the ALPACA bandwidth in dB.
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[^2-SFDRdB]: SFDR specified in units of dB*Hz^(2/3). Put in units of dB by subtracting 57.5 dB, which is 2/3 the ALPACA bandwidth in dB. |
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\ No newline at end of file |