Radio Spectrum Measurement System (RSMS Program)

Radio Spectrum Measurement System (RSMS) Program

RSMS Calibration:

RSMS Gain and Noise Figure Calibration:

Introduction:

Measurement system calibration is performed prior to and during every RSMS site survey. Calibration curves, as in Figure 1, showing system noise figure and gain corrections as a function of frequency across a selected range are generated. As measurements are performed, gain corrections are added automatically to every sampled data point. Gain and noise figure curves are used by RSMS operators to determine the relative health of the measurement system, and to pinpoint locations in the measurement system RF path that are operating suboptimally.

RSMS calibrations are performed automatically with noise diodes such as the one shown in Figure 2. Although the technique of noise diode calibration is not as well known in electrical engineering activities as other techniques (e.g., signal generators or vector network analyzers), noise diodes are commonly used for calibration of measurement systems where minimal size, weight, and power consumption are crucial. Noise diodes provide these features while maintaining adequate calibration accuracy and this is why they are used for RSMS calibrations. ¹ This document describes the theory and operation of RSMS noise diode calibrations.

Theory:

RSMS calibrations are implemented as a variant of the Y-factor calibration method [1]. The Y-factor method of amplitude calibration provides for a simple, yet accurate characterization of the amplitude response and noise figure of an RF receiver system. Using noise diodes, amplitude uncertainties of 1 dB in calibration may be achieved in field calibrations over a frequency range of more than 18 GHz.

The noise diode calibration of a receiver tuned to a particular frequency may be represented in simple, lumped-component terms as in Figure 3. In this diagram, the symbol labeled S represents a power-summing function that linearly adds any power at the measurement system input to the inherent noise power of the system. The symbol labeled g represents the total gain in the measurement system. The measurement system noise factor is denoted by nf_s, and the input is a noise diode with an excess noise ratio of enr_d.²

Note that in this appendix, all algebraic quantities denoted by lower-case letters, such as "g," represent linear units. All algebraic quantities denoted by upper-case letters, such as "G," represent decibel units. Lower-case and upper-case quantities are connected to each other by the relation (UPPER CASE TERM) = 10log(lower case term); for example, G = 10log(g), or if enr_d = 100 mW, then ENR_d = 20 dBm.

In noise diode calibration, the primary concern is the difference in output signal when the noise diode is switched on and off. For the noise diode = on condition, the linear expression is:

p_on = (nf_s + enr_d) × gkTB,

(E1)

and for the noise diode = off condition:

p_off = (nf_s) × gkTB.

(E2)

The quantity k is Boltzmann's constant, equal to 1.38 10^-20 mW s/K (milliwatt seconds per kelvin). T is the system temperature in kelvin, and B is the bandwidth in hertz. The ratio of these two quantities is called the Y factor:

y = (p_on/p_off) = (nf_s + enr_d)/(nf_s)	(E3a)
Y = 10log(y) = 10log(p_on/p_off) = P_on - P_off.	(E3b)

From equation (E3), the system noise factor can be solved as:

nf_s = (enr_d)/(y-1).

(E4)

The measurement system noise figure is 10 log of the noise factor:

NF_s = 10log(enr_d/(y-1))	(E5)
= ENR_d - 10log(y-1)
= ENR_d - 10log(10^Y/10 - 1).

Solving equations (E1) and (E2) for gain (g) yields:

g = (p_on - p_off)/(enr_d × kTB)	(E6a)
G = 10log(p_on - p_off) - 10log(enr_d × kTB)	(E6b)
= 10log(10^Pon/10 - 10^Poff/10) - ENR_d - 10log(kTB).	(E6c)

In RSMS calibrations, equation (E6c) is used to calculate gain from measured noise diode values. Note that this calculation uses the difference between p_on and p_off, rather than the y-factor ratio of these values. Thus, the RSMS noise diode calibration is a variant of the standard y-factor calibration technique.

Although equation (E5) could be used to calculate measurement system noise figure, the implementation in RSMS software uses an equivalent equation. It is derived from (E1):

nf_s = p_off/gkTB	(E7a)
NF_s = 10log(p_off) - 10log(gkTB)	(E7b)
= P_off - G - 10log(kTB).

Substituting expression (E6b) for gain into (E7b) yields:

NF_s = P_off + ENR_d - (10^Pon/10 - 10^Poff/10).

(E7c)

In RSMS calibrations, equation (E7c) is used to calculate noise figure. Whenever an RSMS calibration is performed, P_on and P_off are measured at 128 frequencies across the frequency range to be measured, and equations (E6c) and (E7c) are then used to calculate system gain and noise figure for each of those 128 calibration points. The result is the gain response and noise figure of the system as a function of frequency for the frequency range of the measurement. Negative values of the system gain are stored in look-up tables, and are added to raw data values as a correction factor. The gain-corrected power values are stored as spectrum survey data.

Incident field strength is not calculated for RSMS spectrum surveys, because signal polarizations are not routinely known. If incident field strength is required, and if appropriate signal characteristics are known, then antenna factors can be included as part of measurement analysis. The conversion from measured power to field strength in free space is:

FS_{free space} = (P_meas) + (77.2 dB) + (20log(f)) - G_iso

(E8)

where

FS_{free space} = incident field strength, dBuV/m;
P_meas = power measured in 50 ohms, dBm, corrected for RSMS path gain calibration;
f = measurement frequency, MHz; and
G_iso = gain of the measurement antenna, dBi (dB relative to isotropic antenna).

Alternatively, if the receiving antenna correction factor (ACF) is known, instead of the antenna gain relative to isotropic, then the incident field strength conversion equation is:

FS_{free space} = (P_meas) + (107 dB) + ACF

(E9)

where

ACF = antenna correction factor, dB.

Application:

Excluding the receiving antenna, the entire signal path within the RSMS is calibrated with a noise diode source both before and during a spectrum survey; a noise diode, such as that shown in Figure 2, is connected at the point where the RF line attaches to the receiving antenna. The connection may be accomplished manually or via an automatic relay, depending upon the measurement scenario. The noise level in the system is measured at 128 points across the desired frequency range with the noise diode turned on (ON) and turned off (OFF). The RSMS control computer stores all of the ON vs. OFF noise diode values. The control computer then uses the measured difference between ON and OFF at each of the 128 calibration points to solve the calibration equations (E6c) and (E7c) shown above. The gain values are inverted in sign to become correction values. The resulting set of 128 noise figure and gain correction values are stored as a function of system frequency in look-up tables on the computer disk. The frequency-dependent gain-correction curve is used to automatically correct the measured amplitudes of all received signals in subsequent measurements. Figure 1 shows the gain-correction curve and noise figure curve for a typical RSMS measurement.

This calibration technique has proven very successful for field-deployed radio spectrum measurement systems. It is a fast way to determine sensitivity and gain-correction values for a measurement system, and it also is very useful for isolating the gains and losses through individual components of the measurement system, such as RF lines and amplifiers. Compared to alternative calibration equipment, such as signal generators or vector network analyzers, noise diodes have several advantages:

The physical size and weight of a noise diode are comparatively small: dimensions are typically less than 5 in long and less than 1 in diameter; weight is a few ounces.
Power consumption is low, at about 50 mA of direct current at a +28 volt potential.
Cost is about $1000 for a noise diode.
Because noise diode sources are inherently broadband (typically 100 MHz to 18 GHz or more), there are no frequency-tracking problems in the calibration, as are enountered with many other calibration techniques.

All of these features lend themselves to measurements in the field, where small size and weight, low power consumption, and simplicity of operation are all at a premium. Moreover the low cost and small requirements for size, weight, and power make it possible to locate several noise diodes at various places in the measurement system to diagnose where system losses are occurring, and to carry spares in the event that a noise diode fails. Noise diodes can themselves be calibrated by such entities as the National Institute of Standards and Technology.

At frequencies below 12 GHz, accuracy of noise diode calibration with spectrum analyzers installed in the RSMS is good to within a decibel. At frequencies from 12-18 GHz, accuracy falls to about ±2.5 dB due to a higher system noise figure. For noise diodes producing an excess noise ratio of about +25 dB, as are used for RSMS measurements, gain and noise figure calibrations cannot be performed in a practical sense if the system noise figure is more than about 30 dB or is less than about 1 dB. This is because the difference between P_on and P_off becomes too small to measure reliably in the first case, and too close to the rated ENR of the noise diode to measure reliably in the second case. Noise diode calibrations will not provide information on phase shift as a function of frequency; if a measurement system must be calibrated for phase shift, then additional or alternative calibration methods must be used.

Reference:

[1] S. Adam, Microwave Theory and Applications, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1969, pp. 490-502.

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