HeterodyneHeterodyne ReceiversReceivers andand ArraysArrays Gopal Narayanan [email protected] Types of Detectors
● Incoherent Detection – Bolometers ➔ Total Power Detection ➔ No phase information – used primarily on single-dish antennas ● Coherent Detection – Heterodyne Receivers ➔ Frequency Conversion ➔ Total Power Detection ➔ Spectral Information Preserved ➔ Phase Information preserved – used in interferometers and single-dish telescopes
ModesModes –– ElectromagneticElectromagnetic DefinitionDefinition
● Propagating Spatial Distribution of Energy in a transmission line or free space ● Does not change its spatial distribution as it travels ➔ Free Space : Simple transverse expansion, but maintains same shape ➔ Bounded Transmission Line : Does not change at all except for getting weaker ● Electric and Magnetic Fields in a single mode oscillate sinusoidally with time and position according to frequency and wavelength
Examples
● Free-space – Gaussian Modes ● Bounded Media – Waveguides ➔ Above cutoff frequency, f C propagating modes ➔ < f C evanescent modes RectangularRectangular WaveguidesWaveguides
“Full-height” Rectangular waveguide =>
a b= 2
Single Mode for: λ/2 < a < λ
λ = 2a Cutoff Wavelength C
For example, let a = 2.54 mm (0.1 inches) λ = 2a = 5.08 mm => f = 59 GHz C C λ = a = 2.54 mm => f = 118 GHz U Single-mode waveguide for 59 < f < 118 GHz (good for 3mm wavelength band) For f < 59 GHz, waveguide's modes are evanescent
For f > 118 GHz, waveguide has more than one mode! Waveguide – Lowest Loss (bounded) transmission line At 100 GHz, waveguide loss ~ 5 dB/m For f < 26 GHz, waveguide size becomes too large Use coax instead.
At 10 GHz, coax loss ~ 2 db/m Coax
FeedFeed HornsHorns
Feed horns: Transition from waveguide to free-space modes. Couples to telescope
Corrugated Horns Vs Smooth Conical Corrugated Pyramidal Horns: Conical ● Beam Pattern Symmetry ● Low Cross-Pol
Electric/Magnetic fields in aperture of smooth horn
In corrugated horns, boundary conditions different at horn walls
DefinitionsDefinitions
● Waveguide : Hollow metal pipe in which signal propagates by multiple reflections from walls. Wave propagates in a particular energy distribution called mode
● RF (Radio Frequency) Amplifier : Device to increase signal power, placed at input of receiver. For f>50 GHz, RF amplifiers have waveguide inputs
● Mixer : Circuit that combines RF signal (small signal) with a local oscillator (LO) (large signal) and produces an output at lower frequency (IF).
● LO : Large monochromatic signal (Large voltage swing causes mixer to become non-linear)
● IF Amplifier : Amplifier that follows mixer. Less expensive. Most of the gain in a typical radio astronomical system
● Spectrometer : Device that splits up the IF band into its frequency components, i.e. Spectrum
NoiseNoise
● All parts of receiver contribute noise ➔ Passive (transmission lines, etc.) ➔ Active (Mixers, Amplifiers, etc.) ● Millimeter & Submillimeter wavelengths – Usual to characterize noise of devices by Noise Temperature ● Even applied to noise sources that are not entirely thermal in origin
Device Noise Noiseless Temperature Equivalent Device = T BB at N BB at 0 K T K N
A noisy device acts as if its input is connected to Device a (virtual) blackbody at a temperature which is the same as the noise temperature of the device – usually shown as in the right figure. T N
MeasuringMeasuring NoiseNoise TemperatureTemperature
T IN Prop hides Gain P ∝ T + T OUT IN N (G), frequency bw, etc. T N Y-Factor Method
Phot Thot TN Thot − YTcold Y = = TN = Pcold Tcold TN Y −1
For example, measure with input Bbs at 290 K (room temperature) and 77 K (LN ), say Y = 2 2 => T = 136 K N At mm and submm wavelengths, blackbodies are available (eccosorb)
Advantages of Y-factor method: ● Requires no knowledge of G and BW ● Only linear detectors required ● Fast and reasonably accurate
QuantumQuantum LimitLimit forfor TT N Coherent Receiver – both amplitude and phase detected
Heisenberg Uncertainty Principle!
h T = ≃5K Q k 100GHz
Rayleigh Jean's Limit, P = kBT , B where B – Bandwidth, T is equivalent blackbody at input B IF Power at output of Receivers: P = GBk(T + T ) IF R B where, G – Gain of receiver T – Equivalent Receiver Noise temperature R T – Equivalent BB temperature at input to receiver B
TypesTypes ofof ReceiversReceivers
1) f < 200 GHz eg. SEQUOIA
3) Bolometer Receivers 2) f > 200 GHz
Schottky or SIS
EntireEntire ReceiverReceiver SystemSystem
SomeSome Examples:Examples: SEQUOIASEQUOIA
World's fastest imaging heterodyne array at 3mm wavelength
● Cryogenic Focal Plane array operating at frequencies of 85 – 115.6 GHz
● 32 pixels in dual-polarized 4 x 4 array. Two dewars with 16 pixels each combined with wire grid
● Uses InP pre-amplifiers with 35-40 dB gain
● Two backend spectrometers per pixel, can be independently tuned within 15 GHz
● Used at the Quabbin 14m telescope as a workhorse instrument for 6 years, will be moved to LMT, once LMT is ready
Redshift Search Receiver for the LMT
Next Lecture
AA 1mm1mm SISSIS ReceiverReceiver forfor thethe LMTLMT
Receiver in the Lab Noise temperature Measurements
Single Pixel 1mm SIS Receiver (dual polarization, sideband separation receiver with IF BW of 4-12 GHz) that will commission the 1mm band at LMT PrinciplePrinciple ofof Down-conversionDown-conversion
IF=∣LO−RF∣
SSB Receiver: Single Sideband
● Only one sideband makes it through the receiver. Other (image) sideband rejection (either quasi-optically or at mixer) DSB Receiver: Both Sidebands are superimposed on each other at IF output Sideband Separation Receiver: Both sidebands converted to different IF outputs
MixerMixer –– ClassicalClassical TreatmentTreatment
Bsin( t) RF Asin(sin( t)Bsin( t) Basically, mixers can be LO RF thought of as switches
Recall the trigonometric identity: Asin( t) LO
cos−−cos sinsin= = − 2 IF ∣ LO RF∣
● Any arbitrary signal can be decomposed to sines by Fourier analysis ● If RF is small-signal, and LO is large signal (usual case), |LO-RF| terms dominate ● Various filters usually kept at the IF side of mixer to eliminate unwanted terms
SSBSSB oror DSB?DSB?
SSB
● Lower Spectral Confusion ● Lower system noise temperature within a given sideband – terminate unwanted SB in a cold load
DSB
● Twice as much spectral data, if care is taken ● Twice as much continuum power ● Receiver has fewer components – less complexity
Sideband Separation
● Best of both worlds! More recent heterodyne receivers use Sideband separation
NoiseNoise TemperatureTemperature BudgetBudget
L L G IN M IF T P OUT
T T T IN M IF Optics Mixer IF Chain
P = G (T + (1/L )(T + (T + T)/L )) OUT IF IF M M IN IN
Receiver Noise Temperature, T = T + L T + L L T R IN IN M IN M IF
For low noise receiver:
● T ⇊ Low emissivity optics IN ● L ⇊ Low loss optics IN ● T ⇊ Low Noise mixer M ● L ⇊ Low conversion loss M ● T ⇊ Low IF Noise Temperature IF TypesTypes ofof MixersMixers
Name of the Game – Nonlinear I-V Curves!
1. Schottky Diode Mixers
I∝e V−1 where e = kT
As T↓ α ↑ => more non-linearity
● Schottky no longer competitive with SIS for f < 800 GHz ● Room temperature mixing possible with Schottky receivers. Used in remote sensing and satellites (like SWAS)
2.2. SISSIS MixersMixers
Superconductor – Insulator – Superconductor Physical Temperature < T typically < 4K N I∝e V
Here, α is very large! Lowest noise between 50 – 1000 GHz
Photon assisted Tunneling
For Nb SIS junctions, 2∆/e = 3mV => Bandgap cutoff frequency given by eV/h = 730 GHz SuperconductorSuperconductor TheoryTheory
BCS (1957) – Bardeen, Cooper and Schreifer Theory of Superconductors
Electrons in normal conductor – repel
Electrons in superconductor – Cooper pair
● Cooper pairs – act as single boson. All Cooper pairs are in single quantum state (do not obey Pauli exclusion principle) at 0 V bias! Noisy tunneling process at 0 V. Needs to be suppressed by applying a magnetic field that breaks these Cooper pairs. ● Conventional Electron Tunneling - referred to as quasi-particle tunneling
SISSIS JunctionJunction GeometryGeometry
IF Power
With LO power Without LO power
cf. CSO Tuning 3.3. HotHot ElectronElectron BolometerBolometer (HEB)(HEB)
Normal Superconducting Normal ● HEB – Newer technology ● Can be used between 100 GHz – 100 THz! ● IF BW depends on thermal Resistive time constant, τo
● Lower => Higher IF BW τo
Superconducting Normal
● Response time and BW are dependent on how quickly hot electrons are moved out of superconductor! ● Two types of HEBs – Phonon cooled HEBs (pHEB) – thin and long, and diffusion cooled HEBs (dHEBs) - thick and short
Diffusion-cooledDiffusion-cooled HEBHEB vsvs PhononPhonon CooledCooled HEBHEB
StateState ofof ArtArt inin HeterodyneHeterodyne ReceiverReceiver NoiseNoise TemperatureTemperature
Zmuidzinas 2002
IFIF AmplifiersAmplifiers
● Amplify down-converted signal from mixer
● Since mixers have conversion loss, fairly important to have low IF noise temperature
● Highest possible gain (to isolate from noise of subsequent stages)
● Cryogenically cooled => low power dissipation requirement
● Well-matched to mixer
● GaAs and InP transistors are used
● High total power stability
● MMICs (Monolithic Microwave ICs) often used
LocalLocal OscillatorsOscillators
● Needed for frequency conversion ● Required power levels varies a few μW to 100s of μW for arrays ● Narrow linewidth, low amplitude and phase noise, phase locking ● Frequency agile to cover large RF bandwidths
Technologies
● Solid state oscillators (eg. Gunn) + freq multipliers (made of diode chains)
● Photonics LO (new technology)
● Quantum Cascade Lasers (developing)
ArrayArray ReceiversReceivers Why heterodyne array receivers?
● Single pixel SIS receivers are approaching quantum limit (esp. at lower frequencies). Remaining limit is atmospheric ● Mapping Speed substantially increased with arrays ● N fold increase in time for an N-element array, also telescope motion is reduced ● Best use of good weather conditions ● Mapping consistency – reduced systematic effects due to pointing offsets, relative calibration
Cons & Challenges
● Complicated ● Expensive ● Tight packing ● Cryogenic cooling capacity ● Delivery of LO Power
SidebandSideband SeparationSeparation MixersMixers
● Single Sideband Mixers reject noise in image sideband – more sensitive!
● Sideband Separation Mixers more desirable – more spectral coverage with no cost in sensitivity
● Waveguide-based sideband separation scheme less bulky, and allows integration compared to quasi- optical methods
OMAROMAR OverviewOverview
● 1mm Array Receiver for LMT
● Dual-polarized 16- pixel array
● RF Bandwidth 200 – 280 GHz
● USB & LSB both available simultaneously 4 – 12 GHz IF Band
● Novel Integrated Mixer-Preamplifier Block Eases Integration
Focal-PlaneFocal-Plane ArrayArray AssemblyAssembly
300K horn 40K horn section section 4K horn section
MPA (Mixer Pre- amplifier Blocks)
Magnet Assembly G10 Thermal Break IF Outputs
LO Splitter Tree
UMassUMass SISSIS LabLab TestTest StationStation
Single-ended SIS mixer- receiver in test dewar
Sumitomo SRDK 415DE closed-cycle 4K test-system