Considerations for digital readouts for a submillimeter MKID array camera

Transcription

1 Considerations for digital readouts for a submillimeter MKID array camera Jonas Zmuidzinas Division of Physics, Mathematics, and Astronomy Caltech MKID readout considerations 1

2 MKID readout considerations 2 MKID: basic principle

3 MKID readout considerations 3 Coplanar waveguide (CPW) resonators

4 MKID readout considerations 4 Frequency multiplexing

5 MKID readout considerations 5 Antenna-coupled submillimeter-wave MKID

6 4 4 dual-color submm MKID array MKID readout considerations 6

7 Frequency response and antenna patterns MKID readout considerations 7

8 Demo at the Caltech Submillimeter Observatory (CSO) MKID readout considerations 8

9 MKID readout considerations 9 The MKID camera for the CSO (NSF ATI + Moore) Jason Glenn, PI; Sunil Golwala, co-pi array = 576 spatial pixels Four colors/bands: λ =1.3, 1.1, 0.85, and 0.75 mm = 2304 MKID resonators Focal plane: 4 4 mosaic of 6 6 ( 4) tiles Each tile has 144 MKIDs total 2.8 MHz per MKID 400 MHz bandwidth per tile

10 MKID readout considerations 10 Proposed 400 MHz bandwidth digital readout scheme

11 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.

12 MKID readout considerations 12 Digital downconverter (DDC) Disadvantage: DDCs are silicon intensive, difficult to pack lots of channels onto FPGA.

13 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.

14 MKID readout considerations 14 A better channelizer (Pentek) The silicon-intensive post-fft digital downconverter is shared (time multiplexed) among the 256 outputs.

15 MKID readout considerations 15 MKID Noise

16 MKID readout considerations 16 MKID Noise: frequency vs. dissipation fluctuations Noise PSD (dbc/hz) Rotation angle (deg) Frequency (Hz)

17 MKID readout considerations 17 MKID Noise: power scaling Sδf0 (1kHz)/f2 0 (1/Hz) nm Al on Si 40nm Al on Si 200nm Nb on Si 200nm Al on Sapphire 200nm Al on Ge Internal Power (dbm)

18 MKID readout considerations 18 MKID submm response vs. microwave readout power Frequency response vs. readout power 1 Optical Power 0.9 normalized f P absorbed (dbm) Conclusion: P µw P submm 10 pw.

19 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 , or in engineering units, around -115 dbc/hz. How low is the ADC noise? Better than -115 dbc/hz?

20 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 = 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 db. The noise power is spread across entire Nyquist bandwidth, ν S /2.

21 MKID readout considerations 21 ADC noise: definition of SNR Note: M-point FFT spreads noise power into M/2 bins.

22 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 = log 10 (72) = 134 dbc/hz. Equivalently, for ν S = 400 MHz, SNR > log 10 (200 MHz) = 51 db,or ENOB = 8.7

23 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 log 10 (2.8MHz) = 51 db. SNR generally decreases with sampling rate, so the requirement above dictates the maximum usable sampling rate.

24 The TI ADS bit, 400 MSPS ADC Note: ENOB = 11.2 > 8.7 MKID readout considerations 24

25 MKID readout considerations 25 SNR plot for TI ADS SNR vs INPUT FREQUENCY AND SAMPLING FREQUENCY f S Sampling Frequency MHz fin Input Frequency MHz SNR dbfs Figure 29.

26 MKID readout considerations 26 SFDR Definition

27 MKID readout considerations 27 Typical spectrum for TI ADS 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 Frequency MHz

28 MKID readout considerations 28 Two-tone spectrum for TI ADS f f IN1 IN2 = 69 MHz, 7 dbfs = 70 MHz, 7 dbfs IMD3 = 97.3 dbfs SFDR = 93.4 dbfs 40 Amplitude db Frequency MHz

29 MKID readout considerations 29 SFDR plot for TI ADS SFDR vs INPUT FREQUENCY AND SAMPLING FREQUENCY f S Sampling Frequency MHz fin Input Frequency MHz SFDR dbc Figure 30.

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.