Considerations for digital readouts for a submillimeter MKID array camera Jonas Zmuidzinas Division of Physics, Mathematics, and Astronomy Caltech MKID readout considerations 1
MKID readout considerations 2 MKID: basic principle
MKID readout considerations 3 Coplanar waveguide (CPW) resonators
MKID readout considerations 4 Frequency multiplexing
MKID readout considerations 5 Antenna-coupled submillimeter-wave MKID
4 4 dual-color submm MKID array MKID readout considerations 6
Frequency response and antenna patterns MKID readout considerations 7
Demo at the Caltech Submillimeter Observatory (CSO) MKID readout considerations 8
MKID readout considerations 9 The MKID camera for the CSO (NSF ATI + Moore) Jason Glenn, PI; Sunil Golwala, co-pi 24 24 array = 576 spatial pixels Four colors/bands: λ =1.3, 1.1, 0.85, and 0.75 mm 576 4 = 2304 MKID resonators Focal plane: 4 4 mosaic of 6 6 ( 4) tiles Each 6 6 4 tile has 144 MKIDs total 2.8 MHz per MKID 400 MHz bandwidth per tile
MKID readout considerations 10 Proposed 400 MHz bandwidth digital readout scheme
MKID readout considerations 11 Issues to consider Digital signal processing algorithm in FPGA Frequency selection, output data rate Noise Dynamic range Spurious frequencies, intermodulation products, etc. Implementation details: location, packaging, power source, communication, computer interface, etc.
MKID readout considerations 12 Digital downconverter (DDC) Disadvantage: DDCs are silicon intensive, difficult to pack lots of channels onto FPGA.
MKID readout considerations 13 FFT Channelizer Advantage: FFT computation scales N log(n). FPGAs are capable of real-time 32k point FFTs at input data rates 2 GSamples/sec. Disadvantage: sinc(x) sidelobes, wide output bandwidth.
MKID readout considerations 14 A better channelizer (Pentek) The silicon-intensive post-fft digital downconverter is shared (time multiplexed) among the 256 outputs.
MKID readout considerations 15 MKID Noise
MKID readout considerations 16 MKID Noise: frequency vs. dissipation fluctuations -50 150 Noise PSD (dbc/hz) -60-70 -80-90 -100 120 90 Rotation angle (deg) 10 0 10 1 10 2 10 3 10 4 10 560 Frequency (Hz)
MKID readout considerations 17 MKID Noise: power scaling Sδf0 (1kHz)/f2 0 (1/Hz) 10 17 10 18 10 19 320nm Al on Si 40nm Al on Si 200nm Nb on Si 200nm Al on Sapphire 200nm Al on Ge 10 20-60 -55-50 -45-40 -35-30 -25-20 -15 Internal Power (dbm)
MKID readout considerations 18 MKID submm response vs. microwave readout power Frequency response vs. readout power 1 Optical Power 0.9 normalized f 0 0.8 0.7 0.6 0.5 0.4-115 -110-105 -100-95 -90-85 -80-75 P absorbed (dbm) Conclusion: P µw P submm 10 pw.
MKID readout considerations 19 HEMT and ADC noise Best case: MKID amplitude noise due to background photon statistics rises above HEMT LNA noise. ADC noise should be kept below HEMT noise, k b T LNA ν, where T LNA = 2 5 K for a modern cryogenic HEMT. Maximum readout power: P (max) µw P submm = ηk B T load f. LNA noise to readout carrier ratio for ν = 1 Hz is: ρ LNA = k BT LNA ν P µw (max) = T LNA ν ηt load f 3 10 12, or in engineering units, around -115 dbc/hz. How low is the ADC noise? Better than -115 dbc/hz?
MKID readout considerations 20 ADC quantization noise, SNR ADC quantization noise, uniform distribution, in LSB= 1 units: σ 2 = 1/2 1/2 x2 dx = 1 12. Maximum signal amplitude is A = 2 N /2 (positive and negative). Signal power for sine wave is P max = A 2 /2 = 2 2N /8. Signal to noise ratio: SNR = P max /σ 2 = 2 2N 12/8 = 2 2N 3/2. Decibels: SNR= 10log 10 (2 2N 3/2) = 6.02N + 1.76 db. The noise power is spread across entire Nyquist bandwidth, ν S /2.
MKID readout considerations 21 ADC noise: definition of SNR Note: M-point FFT spreads noise power into M/2 bins.
MKID readout considerations 22 ADC dynamic range requirement The best noise to carrier ratio that an ADC can achieve for a 1 Hz bandwidth is given by ρ (min) ADC = 1 0.5ν S SNR. This quantity is a measure of the dynamic range of the ADC. Frequency multiplexing of N c carriers requires carrier power at the ADC input to be reduced to P max /N c (the carrier powers add since frequencies are incommensurate). For N c = 144/2 channels, we need: ρ (min) ADC < ρ LNA/N c = 115 10log 10 (72) = 134 dbc/hz. Equivalently, for ν S = 400 MHz, SNR > +134 10log 10 (200 MHz) = 51 db,or ENOB = 8.7
MKID readout considerations 23 ADC dynamic range requirement, part 2 More generally: SNR 1 0.5ν S N c ρ LNA However, resonator frequency spacing ν c needs to be kept constant. Therefore: SNR 1 ν c ρ LNA For ν c = 2.8 MHz, SNR 115 10log 10 (2.8MHz) = 51 db. SNR generally decreases with sampling rate, so the requirement above dictates the maximum usable sampling rate.
The TI ADS5474 14 bit, 400 MSPS ADC Note: ENOB = 11.2 > 8.7 MKID readout considerations 24
MKID readout considerations 25 SNR plot for TI ADS5474 400 350 SNR vs INPUT FREQUENCY AND SAMPLING FREQUENCY 70 69 68 f S Sampling Frequency MHz 300 250 200 150 70 70 69 68 68 67 100 69 70 69 68 40 10 100 200 300 67 66 400 500 600 fin Input Frequency MHz 54 56 58 60 62 64 66 68 70 SNR dbfs Figure 29.
MKID readout considerations 26 SFDR Definition
MKID readout considerations 27 Typical spectrum for TI ADS5474 0 20 SPECTRAL PERFORMANCE FFT FOR 130 MHz INPUT SIGNAL SFDR = 78.5 dbc SNR = 70.1 dbfs SINAD = 69.5 dbfs THD = 77.4 dbc 40 Amplitude db 60 80 100 120 0 20 40 60 80 100 120 140 160 180 200 Frequency MHz
MKID readout considerations 28 Two-tone spectrum for TI ADS5474 0 20 f f IN1 IN2 = 69 MHz, 7 dbfs = 70 MHz, 7 dbfs IMD3 = 97.3 dbfs SFDR = 93.4 dbfs 40 Amplitude db 60 80 100 120 0 20 40 60 80 100 120 140 160 180 200 Frequency MHz
MKID readout considerations 29 SFDR plot for TI ADS5474 400 350 85 SFDR vs INPUT FREQUENCY AND SAMPLING FREQUENCY 80 77 73 80 77 70 65 f S Sampling Frequency MHz 300 250 200 150 85 85 85 80 77 80 77 73 70 65 100 85 85 40 10 100 200 73 80 77 70 65 60 300 400 500 600 fin Input Frequency MHz 50 55 60 65 70 75 80 85 90 SFDR dbc Figure 30.
MKID readout considerations 30 Conclusions Digital readout for 144 channel MKID array looks highly feasible. Need ENOB = 8.7 bits and SNR = 51 db, doable at 400 MSPS. ATMEL/e2V has a 2 GSPS, 10 bit digitizer but with SNR = 40 db and ENOB = 6.4 bits. Not quite good enough! Output data rate around 100 Hz is fine. Hybrid FFT/DDC channelizer demonstrates required channel count. Spurs, harmonics, intermodulation products, etc. need to be investigated, but most likely OK. Modulation of sky signal will remove offets. Hit probability is low, 0.5N c (N c 1) 100 Hz/400 MHz = 0.25%. Walsh function carrier modulation could be implemented.