- Introduction
- Frequency range
- Input Noise Temperature
- Harmonics
- Third-Order Intermodulation Products
- Dynamic Range

Because of their low loss, optical fibers are becoming quite popular in radio astronomy for the transmission of wideband RF and IF signals over distances greater than about 100 meters. Since the fiber modems are then an integral part of a radio astronomy receiver we need to look carefully at their signal transfer characteristics. This note reports on noise figure and distortion product measurements of a single-mode fiber transmitter/receiver pair made by Anacom Systems Corporation, model AC106T, that is specified to carry RF signals between 100 and 1000 MHz.

The purpose of this report is to outline the dynamic range considerations that must be taken into account when using fiber modems in radio astronomy applications, particularly when strong RFI signals may be present in the modem passband. In the last section I suggest a dynamic range figure of merit that can apply to radio astronomy receiver components and compare the fiber modem to a couple of commercial low noise amplifiers.

The frequency range specified by Anacom Systems for the AC106T modem is 100 to 1000 MHz, but the two modems tested have very nearly constant gain from 20 MHz or below to at about 1800 MHz as hown in Figure 1. The link gain is guaranteed to be greater than -5 dB and is typically 0 dB with no fiber loss. All measurements were made with a fiber length of 20 meters, which has essentially no loss.

Anacom Systems specifies the modem output noise floor to be -130 dBm/Hz, typical. This is equivalent to a noise temperature of 7.2x10^6 Kelvins. I used the measurement setup shown in Figure 2 to make a rough verification of the quoted noise spec. The method is to add noise to the input of the modem until its noise output increases by 3 dB at a chosen frequency. The noise temperature of the modem is then equal to the added noise.

The noise source is a pair of Minicircuits ZFL-1000LN low noise amplifiers in series with the first amplifier terminated with 50 ohms at room temperature. Minicircuits specifies a noise figure of 2.9 dB (275K) for these amplifiers to which is added the nominal temperature of the termination (295k) for a total input noise temperature of 570K. The second amplifier adds only about 2K so its contribution is ignored. These amplifiers are specified only to 1000 MHz so their noise temperature may be somewhat higher above this frequency.

Approximate noise temperature measurements of the modem pair S/N 2x9903003 were made at 6 spot frequencies between 50 and 1500 MHz. The results are shown in Table 1. The amplifier gains were measured with a CW signal at the quoted frequencies. The computed modem noise temperatures in the table are then

Tmodem = 570K * 10^(0.1 * ((Ampl. Gain) - Attenuation))

Since the attenuators could be set to only the nearest 1 dB the computed temperature are uncertain by about 20%. The average measured temperature up to 1200 MHz is 3.5x10^6 Kelvins or -133.1 dBm/Hz. This is agrees well with the manufacturer's measured value of -134.0 dBm/Hz for this unit.

Table 1. Fiber Modem Noise Temperature Measurements Amplifier Attenuation for Computed Modem Frequency Gain 3 dB output change Noise Temperature 50 MHz 44.8 dB 6 dB 4.3 x 10^6 K 200 44.0 7 2.9 500 45.2 7 3.8 800 44.8 7 3.4 1200 43.6 6 3.3 1500 41.6 2 5.2

The test setup for measuring harmonics generated by the modem pair S/N 2x9903003 is shown in Figure 3. The filters reduce the effects of harmonics generated by the signal generator and the spectrum analyzer.

The second harmonic was measured by setting the signal generator frequency to 200 MHz. The strength of the second harmonic as a function of fundamental signal level at the input to the fiber modem transmitter is shown in Figure 4. When the modem pair was removed from the signal path the second harmonic was about 75 dB below the fundamental at 0 dBm.

The top line in Figure 4 is the fundamental frequency signal level locus with a slope of one. The bottom line is the second harmonic level locus. Since the second harmonic is a second-order product its strength should increase by 2 dB for each dB of fundamental level increase, hence, its locus has a fixed slope of 2 and was adjusted vertically to match the measured data points. The intercept of the two loci is +45 dBm, and the relationship between the fundamental and second harmonic signal level strengths is

Second Harmonic Level = 2 * (Fundamental Level) - 45 dBm

The third and fourth harmonics were more difficult to measure because the lowpass filter did not offer quite enough isolation to cleanly attenuate the harmonics produced by the signal generator. With a fundamental frequency of 133.3 MHz the 400 MHz third harmonic levels were -67 (noisy), -61, -49, and -36 dBm for fundamental levels of +3, +4, +5, and +6 dBm, respectively. With the modem pair removed from the signal path and the same fundamental signal levels, the third harmonic levels were -75 (noisy), -70, -58, and -44 dBm, respectively. The modem-generated third harmonic was about 9 dB above the signal generator harmonic, so the measurements are reasonably reliable. Because the fiber modem is becoming very non-linear for input levels above 0 dBm it doesn't make sense to extrapolate these measurements to lower fundamental input levels. We can say, however, that the third harmonic will be more than 70 dB below the fundamental for input levels below +2 dBm.

Measurements of the fourth harmonic were a bit more problematic because it was about 5 dB weaker than the third harmonic. Fourth harmonic signal levels from the fiber modem pair were -73 (noisy), -66, -54, and -40 dBm for fundamental levels of +3, +4, +5, and +6 dBm, respectively. Fourth harmonic levels without the modem pair were <-76, -75, -63, and -45 dBm, respectively. Again, we cannot extrapolate these numbers to lower fundamental signal levels, but we can say that the four harmonics is at least 75 dB below the fundamental for input levels below +2 dBm.

The standard spec for RF component dynamic range is the third order intercept in dBm. This is usually determined by injecting two signals of slightly different frequency but the same power level and measuring the level of the mixing products of the second harmonic of each signal with the fundamental of the other as shown in Figure 5. For this test the signals were placed at 248 and 252 MHz, and the third-order products were, therefore, at 244 and 256 MHz. The bandpass filter prevented any second harmonic from either signal generator from reaching the modem and spectrum analyzer.

The measured levels of the third-order products as a function of the level of either fundamental signal are shown in Figure 6. The third-order product is expected to increase by 3 dB for a 1 dB increase in fundamental level so the bottom line is matched to the measured data with a fixed slope of 3. The top line is the locus of the fundamental signal level with a slope of unity. The intercept is +31.5 dBm, which is quite close to the manufacturer's measured value of +30.0 dBm. The guaranteed value is +20 dBm. Using our measured value the third-order product level is given by

Third-Order Level = 3 * (Fundamental Level) - 63 dBm

The dynamic range of an RF component or system can be defined in many different ways depending on the specific application. Here we shall compute two measures for the fiber modem, and I'll suggest a dynamic range figure of merit for comparing it to other components in a radio astronomy receiver.

With a noise power density of -133 dBm/Hz and a 3-dB bandwidth of about 1800 MHz the total output noise power with no input to the Anacom Systems AC106T fiber modem is -40.4 dBm. In a radio astronomy system we want the modem to contribute less than 1% to the system noise temperature. If the whole bandwidth were used, this would mean running the modem at a total noise power level of -20 dBm. The leaves about 20 dB of headroom below 0 dBm where the second harmonic distortion becomes significant. If the receiver noise is confined to a smaller bandwidth, the headroom is increased proportionately. A bandwidth of 100 MHz will have a margin of about 33 dB.

The harmonics and third-order intermodulation products are important for narrow band signals in the modem passband. We can compute the minimum detectable narrow band signal level for a sensitive radio astronomy measurement and see what signal level we can tolerate before its second harmonic or third-order product rises above this detection threshold. If we assume a bandwidth of 1 kHz and an integration time of 2000 seconds (33 minutes), the rms measurement noise will be 31.5 dB below the noise power in 1 kHz. With a modem input noise level of -110 dBm/Hz (-80 dBm/kHz) our -31.5 dB corresponds to a power level of -111.5 dBm.

From the second harmonic and third-order level equations above, the spurious signal limit of -111.5 dBm requires the the fundamental signal level be below -33.2 and -16.2 dBm, respectively. The second harmonic can be the more troublesome when the modem is required to carry a passband greater than one octave.

Since the minimum power level operating point of an RF component is proportional to its output noise power, and its maximum signal capacity is proportional to either its second-harmonic or third-order intercept point, also measured at the component's output, we can define a dynamic range figure of merit as follows:

Dynamic Range = Intercept - 10 * log(Input Noise Temp) - GainA more positive value is better. This figure of merit, using the third-order intercept, is listed in Table 2 for the measured values of the fiber modem, for the 0.1 to 1000 MHz amplifier used in the noise measurements test above, and for a Minicircuits 800-1200 MHz high dynamic range amplifier.

Table 2. Comparison of Dynamic Range Figures of Merit. Component Figure of Merit AC106T Fiber Modem -33.5 dB ZFL-1000LN Amplifier -30.4 ZHL-0812HLN Amplifier -14.8

Last modified March 9, 1999