Note for ASTR 518 with Professor Rieke at UA
Note for ASTR 518 with Professor Rieke at UA
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Coherent Receivers 0 Principles gt Downconversion Heterodyne receivers migtlt signals of different frequency if two such signals are added together they beat against each other The resulting signal contains frequencies only from the original two signals but its amplitude is modulated at the difference or beat frequency this downconverted beat signal is used for the detection Unlike incoherent detectors this signal encodes the spectrum of the incoming signal over a range of input frequencies and also retains information about the phase of the incoming wavefront This extra information allows efficient spectral multiplexing many spectral elements observed simultaneously with a single receiver and very flexible use of arrays of telescopes and receivers for interferometry 3 52 31 R m A A A l K l l i I i 1 l n l u l I i H i I i 39 U A l l 0 l A My 1 l l i x l n l l I l i z I l i l i V I A l I Jg J 1 x VHJ v a 2 o For heterodyne operation the mixed field must be passed through a nonlinear circuit element or mixer that converts power from the original frequencies to the beat frequency In the submillimeter and millimeter wave and radio region this element is a diode or other nonlinear electrical circuit component For visible and infrared operation the nonlinear element is a photon detector sometimes also termed a photomixer If the mixer has a linear l chne then the conversion efficiency is zero Similarly any mixer having a characteristic cune that is an odd function of voltage around the origin will have zero conversion efficiency if operated at zero bias Much greater efficiency is achieved however with a characteristic curve that is an even function of voltage if cc V2 the output current is proportional to the square of the signal amplitude loc V2 DC 2 0C P where g is the strength of the electric field hence we prefer to use square IaW devices as fundamental mixers because their output is linear with input power I I I A v v v va va3 xv2 a linear b cubic c quadratic Assume that we are using a mixer illuminated with a mixture of two sources of power one a signal at frequency 005 and the other at wLo Let the power at wLo originate from the local oscillator LO within the instrument We also specify that 005 gt wLo Then the mixed signal will be amplitude modulated at the intermediate frequency 00m loos bowl The signal at 00m contains spectral and phase information about the signal at 005 The signal has been downconverted to a much lower frequency than 005 or mo in the frequency range where it can be processed by Lo input voltage amplitude Lo39 DIP DLo wlF l l conventional electronics Sidebands There is no way of telling in the mixed signal whether Us gt Mo or wLo gt 003 Because we have lost the initial information regarding the relative values of Us and Mo many of the derivations of receiver performance will assume that the input signal contains two components of equal strength one above and the other below the LO frequency wLo Since the signal at wIF can arise from a combination of true inputs at Mo bow and Mo wIF it is referred to as a double sideband signal When observing continuum sources the ambiguity in the frequency of the input signal is a minor inconvenience When observing spectral lines the image frequency signal at the offline sideband results in complications Heterodyne Receivers Mixer At the highest frequencies at which heterodyne receivers are used a continuous wave CW laser is used as the local oscillator The laser light and the signal are combined by a beam splitter sometimes called a diplexer The output is mixed in a photon detector a photoconductor photodiode photomultiplier or bolometer Because a photomixer responds to power or field strength squared it is a square law mixer by definition However such heterodyne receivers are uncommon The technique comes into its own in the submm and at lower frequencies where the mixer is a specialized electrical element onto which the energy SIS junctions tuning inductor lF feed impedance transformers twin slot antenna is concentrated by antennae waveguides and other nonfocussing optics The picture above is a SIS mixer block The local oscillator and the input signal are coupled into the mixers by the twin slot antenna The IF is taken out to the right while the volume to the left helps tune the response for efficiency but at a specific frequency SIS stands for quotsuperconductor insulatorsuperconductor A sandwich of these materials produces the quotdiode or other nonlinear devicequot described above as the heart of a mixer lts operation is illustrated below emptyJLS I S L L states 4 I 2A EF 2A L f d a2 2 v gt lt l densities of a states b c a shows the device without a bias voltage The superconductors are shown in the band diagram approximation the band gap is a few meV A bias has been applied in b When it becomes big enough to align the quotvalencequot band on the left with the quotconductionquot one on the right suddenly Cooper pairs tunnel through the insulator efficiently causing a current See the plot in c for the overall behavior Because the inflection in the bias curve is so sharp at 2Aq relatively little local oscillator power is needed to get a good lF signal However the tuning required for good signal coupling generally restricts the operation to a relatively narrow spectral range 1020 The full receiver is shown below laser photons signal photons combined beam photomixer spli el IF de39ecmr amplifier output Using the photodetector case as an example the mixer need not respond fast enough to track the frequency of the two input signals so those signalsjust produce constant photocurrents In addition the photocurrent contains a component oscillating at the intermediate frequency w ws w The IF current is the heterodyne signal and has a meansquare amplitude of 2 ltIIFgt721LIS 1 where IL is the current in the detector from the LO signal and Is is that from the source It is important to note that the signal strength in equation 1 depends on the LO power As a result many forms of noise can be overcome by increasing the output of the local oscillator The ability to provide an increase in power while downconverting the input signal frequency is characteristic of quantum mixers such as the photomixers discussed here The conversion gain is defined as the IF output power that can be delivered by the mixer to the next stage of electronics divided by the input signal power Classical mixers do the downconversion without gain but the use of very low noise electronics in the GHz range of the IF signal makes it useful to carry out this operation even without gain Post mixer Electronics The heterodyne signal derived above is a low level high frequency AC current it needs to be amplified and converted into a slowly varying voltage that is proportional to the timeaveraged input signal power The first step in this process is amplification We want to presene as high an IF frequency range as possible since the spectral band over which the receiver works is just 2 Af assuming we use it double sideband The best performance for the IF amplifier is obtained with high electron mobility transistors HEMTs built on GaAs The HEMT is based on the metalsemiconductor field effect transistor MESFET It consists of a substrate of GaAs with an ndoped layer grown on it to form the channel with contacts for the source and drain and a gate formed as a Schottky diode between them on this layer The electron flow between source and drain in this channel is regulated by the reverse bias on the gate as with the JFET with an adequately large reverse bias the depletion region grows to the semiinsulating layer and pinches off the current Because this structure is vew simple MESFETs can be made extremely small which reduces the electron transit time between the source and drain and increases the response speed source gate drain ndoped GaAs depletion region semifinsulating GaAs GaAlAs GaAs W In the HEMT the MESFET performance is further improved by using a heterojunction iunction between two different semiconductors with different bandgaps so the electrons flow in undoped GaAs To achieve this result the MESFET is grown on heavily doped GaAlAs whose Fermi level lies above the bottom of the conduction band in the undoped GaAs layer Thus the conduction electrons collect in the GaAs and ow through it under the influence of the MESFET elds The very high mobility in undoped GaAs makes for very fast response to 1011 Hz source gate drain lamp Vi h l L 1 doped m GaAIAs electrons undoped GaAs semiinsulating GaAs DetectorStage The conversion to a slowly varying output can be done by a detector stage that rectifies the signal and sends it through a lowpass filter We would like the circuit to act as a square law detector because ltln2gt is proportional to Is see equation 1 which in turn is proportional to the power in the incoming signal CB R 39 39 39vvvi l I I I IF detectorT C 2 VI WNW detector Iilter integrator section section To demonstrate how the detector stage achieves this goal we solve the diode equation for voltage and expand in M0 2 3 4 VJLHIHLJJILLPI AH 71H 2 q 10 qrozro 310 410 The first and third terms in the expansion will have zero or small conversion efficiency and the 4 h and higherterms will be small if ltlt la Thus the detector stage does act as a square law device Sometimes it is desirable to carry out a variety of operations with the IF signal itself before smoothing it For example imagine that the heterodyne signal is sent to a bank of narrow bandpass electronic filters with a smoothing circuit on the output of each filter The frequencies present at the input to the filter bank are limited to the bandwidth of the IF amplifier or of the photomigtlter typically 1 GHZ The filters can be tuned to divide this IF signal into components at a range of frequencies over the IF stage bandpass Because the intermediate frequency goes as ws w the frequencies in the heterodyne signal correspond to a similar range of frequencies in the source centered on the signal and image frequencies The filter bank therefore provides the spectrum ofthe source under study gt Local Oscillator V At the high frequencies of the infrared and visible regions the only local oscillator with reasonably high power output is a continuous wave laser In the submm and lower frequencies tunable LOs are available usually by starting with a lower frequency oscillator and multiplying it up to the operating frequency In any case LO power is a critical asset Fundamental limits Bandwidth The spectral bandwidth of a heterodyne receiver is determined by the achievable bandwidth at the intermediate frequency Throughput The signal photons cannot be concentrated onto the mixer in a parallel beam even for a point source they will strike it over a range of angles The requirement that interference occurs at the mixer between the laser and the signal photons sets a requirement on the useful range of acceptance angle for the heterodyne receiver This condition can be expressed as q z 3 we where D is the diameter of the telescope aperture and lt1gt is the angular diameter of the eld of view on the sky Thus a coherent receiver must operate at the diffraction limit ofthe telescope laser wavefront signal wavefront A second restriction is that the interference that produces a heterodyne signal only occurs for components of the source photon electric field vector that are parallel to the electric field vector of the laser power ie only a single polarization of the source emission produces any signal The relation between wavelength and etendue and the constraints on polarization are manifestations of the antenna theorem applicable to all heterodyne receivers gt Signal to Noise and Detection Limits The detection limits of a heterodyne receiver are considered differently than for incoherent detectors We need to distinguish noise 1 that is independent of the LOgenerated current IL and 2 that depends on IL In principle the first category can be eliminated by using a local oscillator with sufficient power to raise the signal strength out of the noise Thus the second category alone contains the fundamental noise limits Two types of fundamental noise are 1 quantum noise in the mixer from the generation of charge carriers by the LO power and 2 noise from thermal background detected by the system The division between the two regimes can often be simplified by stating that for by gtgt kTB the quantum limit holds while for by ltlt kTB we get the thermal limit Here TB is the temperature associated with the background power gt Noise temperature To describe the performance on continuum sources a thermal source is introduced through a noise temperature TN defined such that a matched blackbody at the receiver input at a temperature TN produces SW 1 The lower TN the fainter a source gives SW 1 and the better is the performance of the receiver so the behavior is again like NEP the smaller the better In the thermal limit if the effective source emissivity 8 1 then by definition TN TB For the ideal double sideband case the quantum limit is TN s 4 The quantum limit expressed in equation 4 can be justified in terms of the Heisenberg uncertainty principle which states that the uncertainty AP in a measurement of power will be AP 5 where At is the observation time Starting with the equation for Johnson noise in a resistor within a frequency bandwidth df and converting to power noise within a time interval At ltPgt Atk TN 6 Setting AP m ltPgt we obtain h V TN T It is often convenient to express the flux from a source as an antenna temperature Ts in analogy with the noise temperatures This concept is particularly useful in the millimeter and submillimeter and radio regions where the observations are virtually always at frequencies that are in the Rayleigh Jeans regime hv ltlt kT In this case the antenna temperature is linearly related to the input flux density P A i2kTS 7 Where AV is the frequency bandwidth To maintain the simple formalism in terms of noise and antenna temperatures it is conventional to use a Rayleigh Jeans equivalent temperature such that equation 7 holds by definition whether the Rayleigh Jeans approximation is valid or not The achievable signaltonoise ratio for a coherent receiver is given in terms of antenna and system noise temperatures by the Dicke radiometer equation T i KiAfIF ADI2 8 Nc Ti where At is the integration time of the observation and K is a constant of order one gt Comparisons with incoherent detectors Equations 7 and 8 give us the means to compare the performance of coherent and incoherent detectors as long as we also keep in mind the bandwidth and single mode detection restrictions that we have already discussed From equation 7 and the definition of NEP the signalto noise ratio with an incoherent detector system operating at the diffraction limit is N 39 NEP 9 S J 2kTS AVAt12 1 Therefore using equation 8 we obtain the ratios of signal to noise achievable with the two types of system under the same measurement conditions NEP M 12 SN c 2 IF 10 SN 1 2 kT AV Suppose a bolometer is operating background limited and we compare its signal to noise on a continuum source with a heterodyne receiver operating at the quantum limit We set the bolometer field of view at the diffraction limit AQ 72 and assume that the background is in the Rayleigh Jeans regime eg thermal background at 270K observed near 1mm The background limited NEP is NEP 2U2 11 The photon incidence rate p can be shown to be 277kT AV B 12 hV If we assume the bolometer is operated at 25 spectral bandwidth AV 025 then SNc 24x106 12 26x1011 4A 13 We have taken the IF bandwidth to be 3 X 109 Hz a typical value Thus the incoherent detector becomes more sensitive near 26 X 1011Hz or at a wavelength just longer than 1mm Actually this comparison is slightly unfairto it since for example it does not have to work at the diffraction limit so it is the detector of choice for continuum detections to wavelengths of2 to 3mm Hence the development of large scale bolometer cameras for mmwave and submm telescopes Of course the coherent detectors are preferred for high resolution spectroscopy and for interferometry