System for measuring noise figure of a radio frequency device

Noise factor of a radio-frequency device under test (DUT) is determined by driving the input of the DUT with a randomly modulated sine wave and measuring the power of a resulting DUT OUTPUT signal within each of a set of equally-sized frequency bands. The noise factor is computed as a combination of the power of the modulated sine wave within each of a plurality of frequency bands and the measured power of the DUT OUTPUT signal within that same plurality of frequency bands.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates in general to systems for measuring the noise 
figure of a radio frequency device and in particular to a system for 
measuring noise figure employing a randomly modulated signal as a device 
stimulus. 
2. Description of Related Art 
Noise figure F, a commonly used measure of the noise produced by radio 
frequency devices, is defined as the signal-to-noise ratio P.sub.SI 
/P.sub.NI of the device's input signal divided by the signal-to-noise 
ratio P.sub.SO /P.sub.NO of the device's output signal: 
EQU F=(P.sub.SI /P.sub.NI)/(P.sub.S0 /P.sub.N0) [1] 
An electronic device has a gain (or loss) G where 
EQU G=P.sub.SO /P.sub.SI [2] 
The output signal noise P.sub.NO of any device includes a component 
GP.sub.NI, the amplified noise in the device's input signal, and an "added 
noise" component P.sub.NA generated by the device itself: 
EQU P.sub.NO =GP.sub.NI +P.sub.NA [3] 
From equations [1]-[3] we have: 
EQU F=1+P.sub.NA /GP.sub.NI [4] 
From equation [4] we see that the value of the noise figure F for a device 
depends on the amount of noise P.sub.NI in its input signal. In order for 
noise figure F to be a meaningful measure of noise a device produces, we 
must standardize the magnitude of the input signal noise P.sub.NI used 
when testing devices for noise figure F. It is also important to use an 
input signal having a relatively small noise power P.sub.NI, since for 
high values of P.sub.NI the quantity GP.sub.NI in equation [4] could 
overwhelm the added noise P.sub.NA, thereby consigning noise figure F to a 
narrow range of values near 1, particularly for high gain devices. By 
using a small standard input noise power we not only standardize the 
meaning of F but we also provide a wide range of possible values of noise 
figure F with which to characterize the noisiness of radio frequency 
devices. 
The standard input signal noise power P.sub.NI used when measuring noise 
figure F is the very small noise power P.sub.0 produced by a resistor 
operating at a room temperature, specifically 290 degrees Kelvin. A 
resistor of any size will generate the same amount of noise power. A 
resistor's noise power P.sub.N is evenly distributed over the radio 
frequency range and has a value in any frequency band of width B that is 
proportional to resistor temperature T, 
EQU P.sub.N =kTB [5] 
where k is Boltzmann's constant. A resistor held T.sub.0 =290 degrees 
Kelvin will accordingly generate a standard noise power P.sub.0 over any 
narrow bandwidth B where 
EQU P.sub.0 32 kT.sub.0 B [6] 
Since P.sub.0 has a relatively small value of 4.004.times.10.sup.-21 Watts 
for each Hertz of bandwidth B, the radio frequency noise generated by a 
resistor at 290 degrees Kelvin makes a suitable power standard for noise 
figure testing. 
Suppose we connect a resistor held at T.sub.0 =290 degrees Kelvin between 
ground and the input of a radio frequency device, for example an amplifier 
of gain G, to be tested for noise figure F. If the resistor is matched to 
the impedance of the amplifier input, Z.sub.in =Resistance, then the input 
signal is only noise from the resistor, its output signal will be a 
combination of an amplified version GP.sub.0 of the input signal P.sub.0 
and the amplifier's own added noise P.sub.NA. By substituting P.sub.0 for 
P.sub.NI in equations [3] and [4] we have 
EQU P.sub.NO =GP.sub.0 +P.sub.NA [7] 
EQU F=1+P.sub.NA /GP.sub.0 [8] 
Substituting equation [7] into equation [8] we have, 
EQU F=1+(P.sub.NO -GP.sub.0)/GP.sub.O [9] 
Since the input signal noise power P.sub.0 =KT.sub.0 B is known over any 
narrow frequency band of interest B, then by measuring the amplifier's 
output power P.sub.NO over that band of interest we can calculate noise 
figure F from equation [9]. 
While the standard precisely defines F, it is not always practical to test 
a device under test (DUT) for noise figure F by applying the signal 
produced by a resistor held at 290 degrees K as a test signal input to a 
DUT. Since the value of F depends on the difference between P.sub.NO and 
GP.sub.0, then when the gain G of the DUT is too large or too small, a 
test signal input of P.sub.0 may produce an output signal power P.sub.NO 
that is too large or too small to be accurately measured. The well-known 
"Y-factor" method determines noise figure F in a manner that satisfies the 
standard definition of noise figure and yet allows us to employ test 
signal powers that may be larger or smaller than P.sub.0. 
In the Y-factor method we measure the power output P.sub.HO of a radio 
frequency DUT when it is stimulated by the noise produced by an equivalent 
resistor at a some "hot" temperature T.sub.H and again measure the DUT 
output power P.sub.CO when the amplifier is stimulated by a resistor at 
some "cold" temperature T.sub.C. We then compute noise figure F from the 
measured values of P.sub.HO, P.sub.CO, T.sub.H and T.sub.C. 
FIG. 1 represents a radio frequency DUT 10 as an ideal (noiseless) 
amplifier 12 having a gain (or loss) G and a noise generator 14 producing 
"excess" noise power P.sub.E. The excess noise power is represented as 
being equivalent to the noise power output of a resistor at some 
temperature T.sub.E : 
EQU P.sub.E =kT.sub.E B [10] 
The output of noise generator 14 drives the input of a summer 16. When an 
external resistor 18 held at a temperature T.sub.I drives another input of 
summer 16, summer 16 adds the resistor's output power P.sub.I =kT.sub.I B 
to the DUT's excess noise power P.sub.E and supplies the result to ideal 
amplifier 12. Amplifier 12 then amplifies its input signal with gain G to 
produce an output signal of power 
EQU P.sub.NO =GkB(T.sub.I +T.sub.E) [11] 
The quantity GkBT.sub.E is simply another way of expressing the added noise 
P.sub.NA produced by device 10. 
The well-known "Y-factor" for a device driven alternatively by noise 
signals from resistors at hot and cold temperatures T.sub.H and T.sub.C is 
defined as 
EQU Y=P.sub.HO /P.sub.CO [12] 
where P.sub.HO is the power of the device output signal produced in 
response to the hot temperature resistor and P.sub.CO is the power of the 
device output signal produced in response to the cold temperature resistor 
over some frequency band of interest. If we substitute P.sub.HO for 
P.sub.NO and T.sub.H for T.sub.I in equation [11] we have 
EQU P.sub.HO =GkB(T.sub.H +T.sub.E) [13] 
If we substitute P.sub.CO for P.sub.NO and T.sub.C for T.sub.I in equation 
[11] we have 
EQU P.sub.CO =GkB(T.sub.C +T.sub.E) [14] 
Substituting equations [13] and [14] into equation [12] and solving for 
T.sub.E we have 
EQU T.sub.E =(T.sub.H -YT.sub.C)/(Y-1) [15] 
Since P.sub.NA =GKBT.sub.E, then from equation [8] 
EQU F=1+P.sub.E /P.sub.0 [16] 
Since P.sub.E =KT.sub.E B and P.sub.0 =KT.sub.0 B then from equation [16] 
EQU F=1+T.sub.E /T.sub.0 [17] 
Substituting equation [15] into equation [17] and rearranging terms, we 
have 
EQU F=[(T.sub.H /T.sub.0- 1)-Y(T.sub.C /T.sub.0- 1)](Y-1) [18] 
Thus with resistor temperatures T.sub.H and T.sub.C known, and with T.sub.0 
a known constant, then we can measure P.sub.HO and P.sub.CO, compute Y in 
accordance with equation [12] and then compute F using equation [18]. Note 
that equation [18] is independent of bandwidth B. As long as the DUT 
output powers P.sub.HO and P.sub.CO are measured over the same bandwidth, 
it is not necessary to know the exact bandwidth over which the 
measurements are taken. 
While this prior art Y-factor method of measuring noise figure F solves 
some problems, it requires the use of two resistors held at two different 
temperatures T.sub.H and T.sub.C or electrically equivalent noise power 
that must be accurately known. Automatic test equipment employing this 
Y-factor method require some means for separately controlling and 
measuring the temperature of the two resistors or generating suitable 
noise levels. 
What is needed is a method of measuring noise figure F. 
SUMMARY OF THE INVENTION 
The present invention is a method and apparatus for testing noise figure F 
of a radio frequency device under test (DUT). In accordance with the 
invention, a radio frequency sine wave signal is randomly (or 
pseudo-randomly) modulated to provide a test signal for which power is 
distributed non-uniformly over the radio frequency spectrum. Thus there 
will be at least two test signal frequency bands F.sub.H and F.sub.C, each 
of width B, that will convey differing signal power levels P.sub.HI and 
P.sub.CI. Powers P.sub.HI and P.sub.CI are equivalent to the thermal noise 
power in bands of width B of signals produced by resistors held at 
differing "hot" and "cold" temperatures T.sub.H and T.sub.C, respectively. 
In particular, 
EQU T.sub.H =P.sub.HI /kB 
EQU T.sub.C =P.sub.CI /kB 
where k is Boltzmann's constant. 
The test signal is applied as an input signal to the DUT and a resulting 
DUT output signal is processed to produce a time domain data sequence 
representing DUT output signal magnitude as a function of time. The time 
domain data sequence is then transformed to a frequency domain data 
sequence representing the power of the DUT output signal carried in 
successive frequency bands of width B. Two values of the second data 
sequence represent output signal powers P.sub.HO and P.sub.CO signal 
carried in the two frequency bands F.sub.H and F.sub.C. A "measured" noise 
figure F.sub.M is then computed as 
EQU F.sub.M =[(T.sub.H /T.sub.0 -1)-Y(T.sub.C /T.sub.0 -1)](Y-1) 
where Y=P.sub.HO /P.sub.CO and T.sub.0 =290 degrees Kelvin. The DUT's noise 
figure F is the computed as 
EQU F=F.sub.M -(F.sub.S -1)/GAIN 
where GAIN is the gain of the DUT and where F.sub.S is the noise figure 
F.sub.S of measurement system itself. When the gain of the DUT is large, 
or when F.sub.S -1 is relatively small, the DUT noise figure F is 
substantially equal to the measured noise figure F.sub.M. 
The method of the present invention is easier to implement within an 
automatic test equipment environment than prior art systems because it 
does not require the use of resistors held at particular temperatures as 
test signal sources. 
It is accordingly an object of the invention to provide a method and 
apparatus for accurately measuring the noise figure of a radio frequency 
device that does not require holding one or more resistors at known 
temperatures. 
The concluding portion of this specification particularly points out and 
distinctly claims the subject matter of the present invention. However 
those skilled in the art will best understand both the organization and 
method of operation of the invention, together with further advantages and 
objects thereof, by reading the remaining portions of the specification in 
view of the accompanying drawing(s) wherein like reference characters 
refer to like elements.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S) 
Noise Figure Definition 
Noise figure F is a commonly used measure of the noise produced by radio 
frequency device under test (DUT). Noise figure is defined as 
EQU F=1+(P.sub.NO -GP.sub.0)/GP.sub.O [19] 
where G is the gain of the DUT, and P.sub.NO is the output signal power the 
DUT would produce within some narrow frequency band of the radio frequency 
spectrum when the DUT is stimulated by a test signal having power P.sub.0 
in that frequency band. In particular the test signal power P.sub.0 is 
defined as the power produced by a resistor at 290 degrees K within that 
narrow band of the radio frequency spectrum, 
Within any narrow band of width B in the radio frequency spectrum, a 
resistor held at some temperature T produces a noise signal having a power 
P in any part of the radio frequency spectrum of bandwidth B of 
EQU P=kTB [20] 
where K is Boltzmann's constant. Since resistor noise power P.sub.0 
produced by a resistor at 290 degrees Kelvin is relatively small and 
predictable, it can make a suitable standard power source when testing a 
radio frequency DUT for noise figure F. 
Y-factor Method 
While equation [19] precisely defines F, it is not always practical to 
directly test a DUT for noise figure F by applying the signal produced by 
a resistor held at 290 degrees K as a test signal input to a DUT. Since 
from equation [19] the value of F depends on the quantity GP.sub.0, then 
when the gain G of the DUT is too large or too small, a test signal input 
of P.sub.0 may produce an output signal power P.sub.NO that is too large 
or too small to be accurately measured. Also it is not always easy to 
accurately determine the gain of the DUT. The well-known "Y-factor" method 
of determining noise figure F allows us to test a DUT in a manner that 
satisfies the standard and yet allows us to use test signal powers that 
may be more suitable than P.sub.0. The Y-factor method also allows us to 
avoid having to measure or know the gain of the DUT. 
In the Y-factor method, the DUT is stimulated with an input test signal 
produced by a resistor held at a known "hot" temperature T.sub.H. The 
output power P.sub.HO of the DUT's output signal within some narrow 
frequency band of width B then measured. The DUT is also stimulated with 
an input test signal produced by a resistor held at a known "cold" 
temperature T.sub.C. The output power P.sub.CO of the DUT's output signal 
is the measured over the same narrow frequency band. The noise figure F of 
the DUT is then computed as: 
EQU F=[(T.sub.H /T.sub.0 -1)-Y(T.sub.C /T.sub.0 -1)](Y-1) [21] 
where 
EQU Y=P.sub.HO /P.sub.CO [22] 
and 
EQU T.sub.0 =290 degrees Kelvin [23] 
The particular values of T.sub.H and T.sub.C can be chosen so that the DUT 
output power levels P.sub.HO and P.sub.HC are within ranges that are 
appropriate for the DUT and which can be conveniently measured. 
Although the Y-factor method frees us from having to use a particular test 
signal power level, certain aspects of the prior art Y-factor method make 
it less than satisfactory for use in an high-speed testing environment. A 
tester using this method would have to be able to precisely adjust the 
noise temperatures to two different values. Any switch that it uses to 
alternately connect the two noise powers to the DUT must be matched to 
their resistances, and the time the tester may require to perform an 
output signal power level measurement for each of two different input 
signal levels can be lengthy. 
In accordance with the invention, the Y-factor method of measuring noise 
figure is improved by using a randomly (or pseudo-randomly) modulated sine 
wave signal as a test signal input to a DUT instead of the output signals 
of hot and cold resistors. 
Tester Architecture 
FIG. 2 illustrates in block diagram form an apparatus 20 for measuring 
noise figure F of a radio frequency device under test (DUT) 26 in 
accordance with the present invention. A binary phase shift keyed (BPSK) 
modulator circuit 22 randomly modulates a single-frequency (suitably 900 
MHz) sine wave signal from a signal source 24 to produce a test signal 
(TEST) input to a DUT 26. DUT 26 amplifies its input TEST signal with a 
gain (or loss) of G to produce an output signal (OUTPUT). A spectrum 
analyzer 28 processes the OUTPUT signal to produce a data sequence (DATA) 
input to a computer 30. Successive data elements of the DATA sequence 
indicate the total OUTPUT signal power included in successive bands of 
width B of the radio frequency spectrum. Computer 30 computes the noise 
figure F of the DUT based on the information contained in the DATA 
sequence and on the characteristics of the TEST signal. 
Test Signal Characteristics 
FIG. 3 is a plot of the power density P'.sub.T (in dBm/Hz) as a function of 
frequency for the TEST signal of FIG. 2. While the power density spectrum 
of the sine wave signal output of signal generator 24 has a single power 
spike at 900 MHz, when we randomly modulate the sine wave signal output of 
signal generator 24, the resulting TEST signal is wideband in nature 
having a power density that is non-zero over a large portion of the radio 
frequency band. The total power P.sub.T contained in any small frequency 
band of width B can be determined by integrating the TEST signal frequency 
spectrum of FIG. 3 over that frequency band. If, for example, the portion 
of the frequency spectrum between 900 and 903 MHz is divided into 
successive frequency bands of uniform width B then total power P.sub.T for 
each band may be found by integrating the TEST signal power density 
P'.sub.T over each band. For a narrow band width of, for example 1 Hz, the 
total power for each band power approximately equal to 1 Hz times the 
power density P'.sub.T Hz at the center of the band. In the 1 Hz wide 
frequency band between 900 MHz and 900.000001 MHz, the total signal power 
P.sub.H is approximately -120 dBm. The same level of power would be 
generated by a resistor held at some "hot" temperature T.sub.H where 
EQU T.sub.H =P.sub.H /kB [24] 
In another band of width B=1 Hz between 902 MHz and 902.000001 MHz, the 
total signal power P.sub.C is approximately -130 dBm, a power level 
equivalent to that generated by a resistor held at some "cold" temperature 
T.sub.C where 
EQU T.sub.C =P.sub.C /kB [25] 
Noise Factor Computation 
As mentioned above, successive data elements of the DATA sequence output of 
spectrum analyzer 28 indicate the total OUTPUT signal power included in 
successive bands of width B of any desired portion of the radio frequency 
spectrum. With bandwidth width B chosen to be 1 Hz, one of those DATA 
sequence values will indicate an output power P.sub.HO of DUT 26 at the 
frequency band between 900 MHz and 900.000001 MHz. Another of those DATA 
sequence values will indicate an output power P.sub.CO of DUT 26 at the 
frequency band between 902 MHz and 902.000001 MHz. Computer 30 obtains 
values of P.sub.HO and P.sub.CO for the two frequency bands from the DATA 
sequence. Computer 30 consults a pre-loaded lookup table for power levels 
of the TEST signal to select TEST signal levels P.sub.H and P.sub.C for 
the same two frequency bands, and then computes the noise figure F of DUT 
26 using equations [21]-[25]. 
Correction for Measurement Noise 
The spectrum analyzer 28 of FIG. 2 produces thermal noise that adds to the 
noise generated by DUT 26. Thus the value of F computer 30 computes from 
equations [21]-[25] is somewhat smaller than the true value of F for DUT 
26. When the measurement system noise power P.sub.M generated by spectrum 
analyzer 28 is significant in compared to the noise power generated by DUT 
26, then the value of F computed from equations [21]-[25] should be 
adjusted to account for the contribution to noise figure F provided by 
measurement system noise. 
Let us define F.sub.DUT as the noise figure of DUT 26 of FIG. 2, F.sub.M as 
the noise figure of the analog portions of spectrum analyzer 28, and 
F.sub.TOT at the total noise figure for the DUT and spectrum analyzer in 
series. It is well-known that for such series connected devices, the 
following relationship holds true: 
EQU F.sub.TOT =F.sub.DUT +[(F.sub.M -1)/G] [26] 
where G is the gain of the DUT. Rearranging equation [26] we have: 
EQU F.sub.DUT =F.sub.TOT -[(F.sub.M -1)/G] [27] 
Thus to determine F.sub.DUT, computer 30 computes noise figure F=F.sub.TOT 
from the DATA output of spectrum in the manner described above, and then 
subtracts the quantity (F.sub.M -1)/G in accordance with equation [27]. To 
determine the value of the quantity (F.sub.M -1)/G computer 30 must know 
the gain G of DUT 26 and the value of measurement system noise figure 
F.sub.M. Systems for measuring the gain G of a DUT are well-known to those 
skilled in the art and are not further detailed herein. To determine the 
value of F.sub.M, DUT 26 is replaced with a conductive path 32 so that the 
TEST signal is applied directly as input to spectrum analyzer 28. When 
computer 30 then calculates a noise figure value F from the DATA sequence 
produce by spectrum analyzer 28 in the manner described above, the 
computed noise figure is measurement system noise figure F.sub.M. 
Noise Factor Averaging 
In the example described above, noise figure F was computed using only two 
data elements from the DATA sequence output of spectrum analyzer 28, the 
two DATA sequence elements indicating the power carried in the two 1 Hz 
OUTPUT signal frequency bands starting at 900 and 902 MHz. However 
computer 30 could compute a noise figure F in the manner described above 
from DATA sequence elements corresponding to any two frequency bands for 
which the TEST signal has differing power levels. Since the DATA sequence 
output of spectrum analyzer 28 includes a large number of data elements 
representing the power levels in many similarly sized frequency bands, 
host computer 30 computes a value of noise factor F for each of many 
different pairs of DATA sequence elements (and their corresponding TEST 
signal power levels P.sub.H and P.sub.C) and then processes the set of 
computed values of F.sub.DUT using a least squares fit (or any other 
well-known averaging method) to produce an output noise figure F.sub.DUT 
that is less prone to error than noise figure value based on only one pair 
of DATA sequence elements. 
FIG. 4 illustrates a spectrum analyzer 28 of FIG. 2 in more detailed block 
diagram form. Spectrum analyzer 28 includes a down converter 40 for 
converting the OUTPUT signal to a signal OUTPUT' having a frequency 
spectrum shifted 900 MHz, a bandpass filter 42 for filtering the OUTPUT' 
signal to remove frequencies outside a range of interest, an 
analog-to-digital converter (ADC) 44 for digitizing the filtered OUTPUT' 
signal at a rate at least twice its highest frequency to produce and 
output data sequence DATA'. The DATA' data sequence represents the 
magnitude of the OUTPUT signal as a function of time over a frequency 
range of interest. A digital filter 46 implements a discrete Fourier 
transform such as the well-known fast Fourier transform (FFT) to convert 
the DATA' sequence into the output DATA sequence representing the power of 
the OUTPUT signal in each of a set equal-sized frequency bands within the 
frequency range of interest. 
In an alternative embodiment of the invention, computer 30 of FIG. 2 
carries out the function of filter 46, by receiving the DATA' output of 
ADC 44 and executing a well-known discrete Fourier transform algorithm to 
convert the time-domain DATA' sequence to the frequency DATA sequence. 
While the forgoing specification has described a preferred embodiment of 
the present invention, one skilled in the art may make many modifications 
to the preferred embodiment without departing from the invention in its 
broader aspects. For example while the test apparatus 20 of FIG. 2 is 
illustrated as employing a 900 MHz sine wave signal generator, other 
signal types and frequencies could be employed. While in the preferred 
embodiment of the invention described herein modulator 22 of FIG. 2 is a 
BPSK modulator, other types of modulators could implement modulator 22, 
including but not limited to, quadrature phase shift keyed (QPSK), 
quadrature amplitude modulation (QAM), frequency modulation (FM), 
amplitude modulation (AM), and vector modulations (I/Q), or any 
combination thereof. The only requirement is that output of signal 
generator 24 be randomly modulated over some radio frequency band of 
interest so that the power density of the resulting TEST signal varies 
with frequency in some known fashion. While spectrum analyzer 28 is 
described as being of a particular type, spectrum analyzers having other 
architectures could be employed provided they produce the DATA sequence 
described above. The appended claims therefore are intended to cover all 
such modifications as fall within the true scope and spirit of the 
invention.