In this section we will explain the path the signal takes from hitting the dish to becoming digitally stored on the local servers at OVRO. The aim of this section is not to give a complete rendering of every detail. We will instead provide an overview necessary to recognize the specific parts of the system where there is potential of generating or amplifying noise to the signal. This noise will have to be processed and filtered in the pipeline, and it is therefore helpful to know from where it arises.
4.2.1 The strength of the signal
As a radio signal hits a telescope it is very weak. The total power from a signal can be calculated by
P =kbT dν (4.1)
wherekb is Boltzmann’s constant,T is the reference temperature and dν is the band-width. For COMAP the signal power the telescope receives is approximately1.4·10−12 W. Before the signal is registered we need it on the order of10−5 W, approximately 10 million times higher. In order to increase the power of the signal, amplifiers are placed throughout the signal path to boost the signal to the desired strength. As there are limits to how much a single amplifier can boost the signal, and since every component
Figure 4.4: Signal flow block diagram from the receiver to the ROACH2. (Courtesy of James Lamb)
in the system drains power from the signal, several of these amplifiers are placed in intervals to obtain the final result.
4.2.2 Units
Instead of using the units W we often use the log ratio decibel (dB) and standardized log ratio decibel-milliwatt dBm. The dB and dBm are defined as
dB= 10 log10P1
P2 (4.2)
dBm= 10 log10 P1
1 mW (4.3)
where P1 and P2 are two different signal power levels. If e.g. an amplifier takes a signal P1 and boosts it to P2 that is 100 times stronger, then the log ratio would be 2 and the dB value would be 20. A change in power is called gain, and in this case the system would have a gain of 20 dB.
The standardized log ratio decibel-milliwatt dBm is similar to dB but instead of relative to the input power P2 it always measures relative to 1 mW. It is often used to follow the power change throughout a system.
The receiver
As light hit the primary dish it is reflected towards the secondary reflector mounted on top of the primary dish. From here the signal is reflected down towards the receiver. The receiver holds the cryostat module which is mounted at the focal plane containing the dual-polarization 19-pixel feedhorns. As the signal reaches the cryostat it gets captured
Table 4.2: Power and gain at amplifiers 1-5 in figure 4.4 for the 26-30 GHz band.
Amplifier 1 2 3 4 5
Gain (dB) 45 33 33 15 15
Pout (mW) 4.54·10−5 4.59·10−3 1.05 1.27·10−1 1.10·10−1 Pout (dBm) -43.43 -23.38 0.22 -8.98 -9.58
by one of the 19 feedhorns and led to a detector that measures an alternating current (AC).
Once the signal is captured by one of the feedhorns, it is sent through a polarizer which separates the signal into two different polarizations. The signal then continues into an LNA which increases the total power output. The LNAs are specifically designed to amplify the signal without significantly degrading the "signal-to-noise ratio" (S/N).
Down-conversion
Once the signal has been amplified in the first LNA it is sent through the first down-converting module (DCM1). The DCM1 are located inside the "saddlebags" which are mounted on the side of the feedhorn plate. The signal is down-converted since lower frequencies are more convenient for the electronics. The DCM1 consists of a mixer (circle with a cross in fig. 4.4) and a local oscillator (LO) operating at 24 GHz (circle with a Tilde-line in fig. 4.4). The "radio frequency" (RF) signal input and the "low frequency" (LO) signal input are sent into a mixer which sends out two "intermediate frequency" (IF) signals. The mixer multiplies the two input sine-waves such that
sin (ω1t) sin (ω2t) = 1
2cos ([ω1−ω2]t)−1
2cos ([ω1+ω2])t. (4.4) whereω1 and ω2 are the frequencies of signal 1 and signal 2 and t is the time.
The result is two different output signals. One signal is down-converted to a fre-quency equal to the difference between the two input signals, and one signal is up-converted to a frequency equal to the sum of the two input signals. The two output signals have the same properties as the input RF signal, only with a different frequency.
The down-converted signal is now in the range 2-10 GHz which is separated into two sidebands covering 2-6 GHz for band A and 6-10 GHz for band B.
Unfortunately, we do not only receive the up- or down-converted frequency signal.
In addition the resulting signal consists of "leakage" from the RF and LO signals, harmonics of the input signal as well as reflections coming back into the mixer from the IF port. The effect is a signal consisting of harmonic content well outside the frequency range of interest. This "noise", together with the up-converted signal, is sent through high-pass filters (boxes with wave lines in fig. 4.4) in order to sort out the desired signal.
The IQ mixer
Another problem when using mixers is image frequencies. If our LO signal has a fre-quency of 10 Hz and the RF signal has a frefre-quency of 5 Hz, the resulting IF signal will have a frequency of 5 Hz. However, if an RF signal would have a frequency of 15 Hz, the resulting IF signal would still be 5 Hz. There is no way of telling these signals apart without further processing of the signal. The reason for this is that we are lacking some vital information regarding our RF signal. Even though the amplitude of the signal and its frequency is known, we have no information regarding the phase of the signal since we have no reference of the phase.
A way to handle this problem is by applying an "in-phase quadrature" (IQ) mixer.
An IQ mixer separates the a signal into two "smaller" signals that are 90◦ out of phase.
This can be done by the use of Euler’s formula
eiωt= cos (ωt) +isin(ωt) =LSB
e−iωt= cos (ωt)−isin(ωt) =U SB (4.5) where ωt is the frequency of the signal, the term cos (ωt) is the I output, the term sin (ωt) is the Q output and LSB and USB are the "Lower sideband" and the "Upper sideband" respectively. We can now sort out the signals that are either above or below the LO by measuring their phase relative to the I signal. This is done in the "second down-converting module" (DCM2) where this information divides each sideband into upper and lower bands thanks to the image frequencies concept. The LO in DCM2 operates at 4GHz for for band A and at 8 GHz for band B resulting in 2 GHz wide I and Q signals in the range 0-2 GHz.
Spectrometers
The IF signal is now sent to the ROACH2 spectrometer which consists of a "analog-to-digital converter" (ADC) as well as a "Field-programmable gate array" (FPGA). Inside the FPGA, for each I and Q, 4×2048 time samples are taken and sent through a "poly-phase filter bank" (PFB) which generates a down sampled time series with 2048 samples and through a "Discrete Fourier Transform" (DFT) yields 1024 frequency channels per sideband. After the DFT the signal is divided into the bands and frequencies displayed in table 4.3, where ∆ν = 1.953125 MHz is the distance between each channel and the counterirepresents channel iin 1024 channels.
Each sideband is now multiplied with its conjugate in order to yield a real positive number, the channel power. This stage is what if often referred to the "detection stage".
The detections are separated into "time series" of 8192 samples each. Each time series consists of 3/4 of the previous time series in addition to 1024 new samples. Over a time of 20 ms these time series are summed up yielding the information which will later become the input data for the pipeline.
Table 4.3: sideband and frequency distribution after signal processing. Due to equal frequencies for channel 0 and LO-pickup leading to corruption in channel 512 these frequencies are always ignored in all sidebands.
A:LSB (28-30) GHz 28.0 - ∆ν (i/1024) A:USB (28-30) GHz 28.0 + ∆ν (i/1024) B:LSB (32-30) GHz 32.0 - ∆ν (i/1024) B:USB (32-24) GHz 32.0 + ∆ν (i/1024)