Radio signals are weak--the total power received from all observed radio sources at all observatories throughout history is scarcely enough to strike a match. A typical radio signal has a power of only 2x10-15W. The need for the amplification of the signal is obvious and is one of the main purposes of the receiving system. The Super Heterodyne Receiving System (SHRS) achieves high amplification while introducing very little internal noise. Each part of the SHRS will be discussed in more detail below, but first a basic overview of the system will be given to provide the reader with some background knowledge.

Although we are only interested in wavelengths of ~7.5cm (~4 GHz), the dish reflects a wide range of wavelengths. Therefore, a large range of signal frequencies is reflected into a waveguide called a horn. The horn is an open-ended cavity which permits standing waves from signals of particular wavelengths to be formed. Due to the nature of this cavity, the horn acts as a preliminary filter, screening out some signals with unwanted frequencies. To first order, the wavelength at which resonance occurs is equal to the diameter of the waveguide. A probe is placed in the horn at an antinode position of the standing wave pattern. There, the signal creates a current in the probe proportional to the intensity of the wave.

The front-end of the receiver system is generally regarded to be those components of the system physically mounted on the antenna itself. From the front-end, the signal is sent to the back-end--that part of the system located elsewhere. Because the impedence of transmission lines increases with frequency, the signal is down-converted at the front-end to a lower frequency, called the intermediate frequency (IF), which is then sent to the back-end with smaller losses. This is the reason for the location of the break between the front and back ends of the receiver system. The square law detector was included in the front-end for this project, although, often the break occurs between the IF amplifier and the square law detector (see the diagram below).

SHDR schematic.

The front-end achieves two important goals: amplification and conversion of the signal to a DC voltage, through four main components, the radio frequency (RF) amplifier, the mixer, the IF amplifier and the square law detector.

A Look at the RF Amplifier, Mixer and Local Oscillator

The RF amplifier does what its name suggests. It operates over a particular bandpass containing the desired radio frequency and amplifies only those input signals with frequencies contained in its range. Ideally the frequency response function of the RF amplifier would be a perfect boxcar function with height of desired gain centered at the observing frequency. Unfortunately the transformation from the ideal world to the real world, produdes a frequency response function that doesn't much resemble a boxcar. It is noteworthy that the RF amplifier noise is usually the predominant noise source in the receiver system. Therefore, effort is spent on minimizing the noise contribution of the RF amplifier.

From the RF amplifier the signal enters the mixer where the conversion of the signal to the intermediate frequency occurs. The mixer accepts two input signals, the actual signal from the RF amplifier, and a signal produced from the local oscillator (LO). The mixer adds these two signals and outputs the square of the sum. The output signal is carried on a frequency given by:

fIF = fRF - fLO.

Because the frequency of the oscillator signal can be arbitrarily chosen, the intermediate frequency can also be chosen. Since the RF amplifier, the mixer and the LO used were combined in a single commercial unit, our oscillator signal cannot be varied. Thus the mixer produces a new signal carrying the same information as the original signal (scaled by a known factor from the LO signal), but with a frequency less than the observing frequency of the horn.

A Look at the IF Amplifier

The signal gets amplified further in the IF amplifier. In order to select the signal with the desired frequency, the IF amplifier has a filter with a narrow bandpass centered on the IF. Its narrow bandpass defines the bandpass of the entire sytem. Signals within this bandpass will be further amplified. A problem arises here due to the nature of the Fourier transform of the signal. If a signal enters with frequency

fRF' = fRF - 2fIF,

then when the LO frequency is subtracted from it,

fRF' = fLO = -fIF,

it also produces a similar IF frequency. The IF signal has contributions from two unique radio frequencies, one from the actual observing frequency, the other from a frequency not desired. The observing frequency is the upper sideband, while the latter is the lower sideband. It is necessary at the RF amplifier stage to filter out this lower sideband to permit only the observing frequency.

A Closer Look at the IF Amplifier

There are two main components to the amplifier, those being the op-amps and the filters. With these two components the primary goals of the amplifier are achieved, namely the amplifying of the signal and obtaining a narrow bandpass about the IF. In the circuit design two amplifiers are used to reach the desired gain. The need for two stages of amplification arises due to the appearance of circuit oscillations if too much gain is present at a single stage. Op-amps used are the MAR-6SM with a gain of 15dB at 1.2GHz and the VNA-25 with a gain of 20dB. Thus while passing through the IF amplifier, the signal receives a gain of 35dB.

The operation of this circuit is fairly straightforward. Ideally we want to pass the IF signal through the two gain stages and through the filters and end up with a high gain in a narrow bandpass. The op-amps need to be powered by external sources of DC voltage; the MAR-6SM needs to operate over a range of 0-12V and the VNA-25 needs to operate over 0-5V. As seen from the schematic, the IF signal enters the circuit riding on the same line as the +18VDC supplied by the DC power supply. Because 60Hz AC has been rectified to produce the DC, there will still be rippling in the DC voltage along with other AC signal interference. Since any signal entering the op-amps will be amplified along with the IF signal, we want to filter out this DC noise. This is done using the LC filters enclosed in Box 1. Because the complex impedance varies with the frequency of the signal, by choosing the values for L and C selectively, unwanted signals can be blocked effectively from entering the gain stages of the circuit. The LC impedance goes to infinity at the resonant frequency given by:

fo = 1/(LC)1/2.

In Box 1 there are two different capactitors, with C1=100uF and C2=100pF. A range in the capacitance is needed in order to set up large impedances for both low and high signal frequencies. A high frequency signal will see a large impedance along the C2 path but a low impedance along the C1 path. The signal will then be grounded out through C1. And vice-versa for low frequency signals. They will see a large impedance along C1, and as such, will be grounded out through C2. The DC signal however with a zero frequency, will see zero impedance and will continue unimpeded towards the MAR-6SM. The 1.0uH inductor below Box 1 along with capacitor C2 prevents the IF signal from travelling back towards the power supply.

The IF signal enters at B sitting on top the DC signal and travels unimpeded to the first gain stage. However before the op-amp are two blocking capacitors with have infinite impedance for the DC signal. Capacitor C3 forms a voltage divider with the 75 Ohm resistor. The voltage divider produces an output voltage of:

Vout = R2(R1 + R2)-1 Vin.

With R1=75 Ohms, and R2=infinity, Vout = 0. Thus the DC voltage is blocked effectively from entering the op-amp, and only the IF signal will be amplified.

As mentioned above MAR-6SM requires +12VDC to operate. This voltage is supplied from the 7812 voltage regulator. The regulator itself has a potential drop of 2V. Thus with +18VDC being supplied to it, the regulator will easily produce the needed +12V for the op-amp. Along the path from the output of MAR-6SM to the voltage regulator a 680uH inductor along with a 0.01uF capacitor prevents the IF signal from travelling back along that route and forces it to continue to the filter PHP-900. PHP-900 is a high-pass filter, theoretically attenuating signals with frequencies below 900MHz. In between this filter and the MAR-6SM is another 100pF capacitor. Since we have a DC signal entering the line at C, this needs to be blocked from continuing onwards.

After the filter, the signal enters a second gain stage, the VNA-25 op-amp. The VNA-25 requires +5VDC to operate, and this is supplied to it by a 78L05 voltage regulator. As with the previously discussed voltage regulator a series of filters is present to clean the DC signal and to prevent IF signal from straying back through the circuit. The IF signal exits the second gain stage with a total amplification from the IF amplifier of 35dB and lastly passes through a hi-pass filter identical to the previous one. The second filter was added in hopes of steepening the frequency response of the system. However, the filters achieved disappointing results compared with specs. The frequency response of the system is discussed in more detail below.

A Look at the Square-Law Detector

Even though the original signal has been down-converted to a lower IF, the frequency of the signal through the electronics is still on the order of a GHz. The system needs some way of detecting this signal to produce a meaningful output. This is the function of the Square Law Detector (SLD).

Radio radiation received at a radio telescope is distributed as white noise. By this, it is meant that the amplitude of the received electromagnetic (EM) wave varies randomly with time. Thus, the amplitudes of the EM signals are distributed evenly about zero. Since observation of astronomical sources requires a finite integration time, measuring only the amplitude of the incoming waves would be problematic since the time average would always be zero for any integration of reasonable duration. However, the variance of the signal will always be greater than zero and therefore will have a non-zero time average. Thus a system that is able to measure the variance of a signal is required.

The signal enters the SLD with a power proportional to the square of the amplitude of the incident EM wave. Through the use of a diode, the SLD outputs a DC RMS voltage level which is proportional to the power of the signals. Details on the diode performance are given in the Diode response section. Because the detector is measuring the variance of the signal, the error of the variance is inversely proportional to the number of events measured. In order to get lower errors in the output signal, it is necessary to use a larger integration time to collect a larger number of events. The noise can also be lowered by integrating over a wider bandpass which also allows a larger number of events to be measured. In summary, the error in the output is inversely proportional to the square root of the integration time and the bandpass.

A Closer Look at the Square Law Detector

Initial designs of the SLD called for a VNA-25 op-amp at the first stage of the detector before entering the diode. This would provide a gain of 20dB to the IF signal. However, after testing the detector, this op-amp was removed due to its large gain. In order for the response of the diode to be linear with respect to its input, the input signal cannot be larger than 0.2V. With the op-amp in place, this limit was exceeded, and the diode operated in a regime where its behavior was non-linear. This omission resulted in a modified circuit design.

The 7805 voltage regulator steps down the +15VDC supply to the necessary +5VDC for the op-amps. Once again the power supply is cleaned with LC filters. The diode permits the current to flow in one direction only. The current allowed through charges the 1500pF capacitor. The RC circuit which follows the diode sets the time constant of the capacitor (t=RC) determining how long it takes the capacitor to charge or discharge to 1/e of its initial charge. With R=1.0M and C=1500pF, this produces a time constant of 1.5msec. The time constant determines how smooth the DC signal is. If the capacitor charges and discharges on time scales large compared with the variability of the input signal, it will have a slow response to any sharp peaks or valleys in the input signal. Since 1.5msec is large compared with the 1.2GHz signal, the capacitor won't "see" short term variability and will roughly stay charged at the same level, smoothing out large scale variations in the signal.

Because the diode outputs a negative voltage, the second op-amp is negatively biased, inverting the signal as it amplifies it to a maximum of +10VDC. The +10VDC is the maximum input to the A/D converter. The gain of the op-amp is the ratio of the feedback resistor, Rf=330K, to the input resistor, Rin=3.3K, a gain of 100dB.

Calibrating the Electronics

The calibration of the electronics entailed measuring the spectral responses of the output as each of the components of the frontend was added to the RF amplifier, as well as the determination of receiver temperature. In order for the calibration process to work, the horn had to be "seeing" a source of uniform temperature for the entire spectrum. Additionally, the behavior of the diode within the square law detector was measured and compared to the manufacturer's specifications.

To perform these tasks, the team was greatly assisted by Fred, who set up the equipment required for the measurements. As for the construction of the electronic devices, the calibrations were done in two groups, each set of measurements were taken twice and compared.

Receiver Temperature

A uniform temperature was acheived using a microwave absorbing foam, which acted to filter out all radio waves which might be present around the horn. The foam was maintained at a constant temperature by placing it over the mouth of a pail which was either empty (i.e. the foam was at room temperature) or filled with liquid nitrogen (i.e. at 77K).

The frequency (or spectral) responses were measured using an oscilloscope. The gains were measured with a digital voltmeter by comparing the output voltages for different foam ambient temperatures. The outputs of the oscilloscope were photographed for later comparison. Photos were taken of the spectral response of the RF ampliifer alone and with the IF amplifier. To measure the effectiveness of the high-pass filters within the IF amplifier, the spectral responses were measured for IF amplifiers constructed both with and without the filters in place. The IF amplifier with the filters was designated IF-1; that without the filters was denoted IF-2.

The first step was to look at the output of the RF amplifier with the horn "seeing" only the room temperature (which was taken to be 20°C, or 293K).

The spectral response of the RF amplifier.

The centre line of the oscilloscope grid is at 950MHz, while the marker (indicated by an obvious dip on the response function) is at 1450MHz. This means that the major scale unit of the oscilloscope's output corresponded to ~200MHz.

Next, the IF amplifiers were independently tested with the RF amplifier. As noted above, the frequency of the RF amplifier output is IF. The spectral responses of IF-1 and IF-2 are:

Spectral responses of the IF-1 and IF-2 amplifiers.

The scale is the same as that of the RF amplifier above. The goal of the filters within the IF amplifer was to reduce the signal transmitted at low frequencies. Since the carrier signal for our telescope will be at 1.2GHz, it was desirable to filter out frequencies significantly lower than 1.2GHz.

Comparison of the spectral responses of IF-1 and IF-2 revealed that this goal was not well achieved by the filters used in our IF-1 amplifiers. There were less low-frequency contributions without the filters than with it! It is worth noting however, that there was a strange discontinuity in the output signal without a filter (IF-2), which could make that result untrustworthy.

In an effort to determine whether or not there was simply a problem with the specific filters installed in the IF-1 amplifier, similar filters were installed in the IF-2 amplifier. This yielded a response which was virtually identical to that of the IF-1 amplifier and further convinced us of the poor quality of the PHP-900 filter.

Inserting an alternate electronics box into the oscilloscope allowed us to examine the spectral responses with the filters for a higher frequency range than the original box allowed. The photographs reveal that the signal decreased reasonably well for frequencies greater than 1.6GHz.

Spectral response of the IF amplifiers at higher frequencies.

After the detector (which was designed to also act as a low frequency amplifier) was added, we checked the variation of the output voltage with temperature by observing the absorbing foam at two different temperatures. Two trials were taken for each temperature. Trial one yielded voltages of 4.85V and 1.80V for 293K and 77K, respectively, while trial two yielded values of 4.65V and 1.70V for the same temperatures.

A plot of the output voltage vs. temperature reveals that a measurement made at zero Kelvin does not give a zero value for the voltage. This voltage offset from zero can be translated to a temperature using the conversion relation obtained from the slope of the graph. Performing these calculations yielded receiver temperatures of 50.5K and 47.5K respectively for the two trials. These corresponded to the receiver voltages fo 0.71V and 0.65V as read from the intercepts of the graph. It was expedient to adopt an accepted value for the receiver temperature of our frontend. The average value of the two trials was 49K, with an uncertainty of at least 1.5K.

Unfortunately, after the electronics had been mounted on the telescope, it was quickly discovered that the MAR-6SM op-amp used in the IF amplifier circuitry was producing too much gain which produced oscillations in the circuit. Thus, the IF amplifier was redesigned and assembled by Fred. Therefore, the spectral responses and receiver temperatures previously discussed are not applicable to the final electronics configuration used on the telescope.

The spectral response of the new IF amplifier was briefly examined before mounting. Due to technical difficulties, it was not possible to obtain photographic representations; however, it was noted that the response revealed larger gains at frequencies below 900MHz where before they had been minimized with the original design.

A measurement of the receiver temperature was not made in the lab, but it was possible to determine during the calibration runs on the telescope (discussed in the section on astronomical Calibration). Such a calibration was performed on April 10, 1996 prior to an observation of the supernova remnant Cassiopeia A. This resulted in a voltage offset of 1.94V and a receiver temperature of 80K.

The choice of which calibration to use as the "accepted" receiver temperature was somewhat arbitrary. Calibrations were not performed for every observation, although ideally they should be. Often, observations were done for other reasons (i.e. calibration of positioning or to find the source) and thus calibrations were not performed. Other calibrations gave receiver temperatures as low as 50K, as mentioned above, and as high as 114K (done for the April 9, 1996 observation of CasA). There seems to be a lot of variation in receiver temperature with amibient temperature. The calibration of April 10 yielded a reasonable value and was performed on a cool day (-0.6°C) which made the results somehow more trustworthy.

We recommend that performing a series of calibrations each day for a week or several weeks would be a worhtwhile exercise, since this could provide some insight into how the receiver temperature varies with temperature (before and after a Chinook would yield a large variation over a short time period). If the variations are truly as acute as our observations imply them to be, calibrations with every observation would be more critical than ever, and faint sources might prove to be more difficult to detect in warm weather.

Response of the Diode

Several points must be raised before discussion of the diode behavior. First, the diode tested was not that which is in the telescope, but one like it from the same manufacturer. We were unable to test the actual one, since Fred had already installed it.) Second, due to technology limitations, the diode could not be tested in the frequency regime in which it will be used. It has already been discussed that the signal carrier frequency of the receiver is 1.2GHz. The tests of the diode were performed at a substantially lower frequency of 70MHz.

The response of the diode was measured for a range of input voltages. The testing was performed by inputting a sinusoidal wave which was rectified by the diode. The output was thus an analog DC voltage. An attenuator was used to achieve as fine a range as possible in the input voltages. The attenuator did not deform the waveshape.

In order to produce a meaningful measurement of the RF signal, the diode must be linear in response to the power input over the range at which it operates. The output of the detector is a DC voltage proportional to the input voltage squared. For engineering purposes, powers are usually expressed in terms of debyes (dBm). Since the input voltage was peak-to-peak, the RMS input voltage had to be divided by root eight. The input power to the detector can be calculated via the expression:

#dB = 20 log(Vin/Vref).

where Vref is 0.225V. This calculation holds true only for 50 Ohm circuts.

The manufacturer's specifications of the diode give the output DC voltages as a response to input powers. Our measurements yielded the following relation:

As the specifications showed, the diode has a regime over which its response is linear. Measurements taken in that regime will yield reliable results.

Once all the components of the receiver had been calibrated, they were affixed to the telescope so that the probe lay as close as possible to the focal plane.