Network for simulating low temperature resistors

A class of two-terminal active networks which simulate low-noise temperature resistors is disclosed. A single field effect transistor or other suitable amplifier comprises the active element of the network. A dual transformer feedback arrangement or a single transformer feedback arrangement comprises the remainder of the circuit. Either positive or negative simulated resistors can be obtained with a wide range of equivalent resistance values and effective noise temperatures.

TECHNICAL FIELD 
This invention relates to single-port electrical networks and more 
particularly to networks which simulate low-noise temperature resistors. 
BACKGROUND ART 
It has long been known that all electrical resistors are characterized by 
an inherent noise which is due to the thermal agitation of the free 
electrons within the resistor material. As used herein, the term 
"resistor", includes any body of material capable of carrying an 
electrical current. As such, the term embraces components such as wires 
and other conductors which are not ordinarily thought of as "resistors". 
If a signal current in the resistor or conductor is smaller than the 
random current due to thermal agitation then, as a practical matter, the 
signal is masked and no amount of amplification can separate them. This 
noise, known as "thermal noise", "Johnson noise" or "white noise", has 
heretofore generally been accepted as one of the limiting factors in the 
design of low-level signal processing circuits. 
From the research of Johnson and Nyquist in the late 1928's, it is known 
that the thermal noise voltage across the open ends of a resistor is 
determined by the formula: 
EQU e.sub.n.sup.2 =4kTRB [1] 
Where e.sub.n.sup.2 is the average of the square of the noise voltage; k is 
Boltzmann's constant (1.138.times.10.sup.-23 joules per K); T is the 
absolute temperature of the conductor in .degree.K.; R is the resistor or 
conductor in ohms; and B is the bandwidth in Hertz over which the noise is 
measured. 
In order to reduce the thermal noise of a given resistance R, it is seen 
from Equation [1] that either the temperature (T) or the bandwidth (B) 
must be reduced. To reduce B, of course, is generally not possible, since 
the operational bandwidth of a circuit is ordinarily predetermined and not 
susceptible to casual manipulation. In general, therefore, it has been the 
practice to minimize the thermal noise of a circuit by cooling the 
resistor or the entire circuit, in some cases to cryogenic temperatures. 
However, since the noise voltage is proportional to the square root of the 
absolute temperature, it is readily appreciated that it is both costly and 
cumbersome to provide the degree of cooling required to achieve a 
significant reduction in thermal noise. 
It is therefore an object of the present invention to provide a 
non-cryogenically cooled low-noise temperature resistance. 
In 1939, it was suggested by W. S. Percival that a simulated resistor 
having an effective noise temperature lower than ambient temperature could 
be realized by feedback means. (See: W. S. Percival, "An Electrically 
`Cold` Resistance", The Wireless Engineer, Vol. 16, May 1939, pp. 
237-240). By utilizing a single transformer between the plate and grid of 
a vacuum tube amplifier, Percival simulated a resistance having an 
effective temperature of 70.degree. K. The same technique was later 
expanded upon by Strutt and Van der Ziel in an article entitled, 
"Suppression of Spontaneous Fluctuations in Amplifiers and Receiver for 
Electrical Communication and For Measuring Devices," Physica, Vol. 9, No. 
6, June 1942, pp. 513-527. Professor Van der Ziel also briefly summarized 
the techniques in his treatise "Noise," Prentice-Hall, New York, N.Y., 
1954, pp. 262 et seq. (See also: U.S. Pat. No. 2,352,956 which issued to 
M. J. O. Strutt, et al. on July 4, 1944. ) 
The circuits of the prior art appear to have received little attention in 
the several decades since their introduction. This may be due to the many 
shortcomings inherent in the use of vacuum tubes such as their high 
operating temperatures and the other sources of noise inherent therein. In 
any event, advances in solid state technology have produced a number of 
sophisticated, highly efficient, low-cost active devices which allow the 
synthesis of economical low-noise temperature resistance simulating 
circuits. 
It is therefore another object of the present invention to provide an 
active circuit which simulates a low-noise resistor. 
A recent attempt at reducing circuit noise by feedback means is illustrated 
in U.S. Pat. No. 3,839,686 which was issued to W. Vogel on Oct. 1, 1974. 
According to the teachings of that invention, the induced voltage on a 
transmission line such as a coaxial cable can be decreased by a feedback 
control circuit which includes an amplifier. Although the circuit of the 
Vogel patent does not simulate a resistance, either low-noise or 
otherwise, it does represent an example of noise reduction employing 
feedback techniques. 
More recent techniques for simulating low-noise temperature resistors have 
been suggested in copending U.S. Patent Applications: Ser. No. 838,511, 
filed Oct. 3, 1977, now U.S. Pat. No. 4,156,859; and Ser. No. 881,296, 
filed Feb. 27, 1978, now U.S. Pat. No. 4,176,331. Another suggested 
circuit which utilizes a feedback amplifier as the active circuit element 
is described in a paper in Radio and Electronic Engineer, Vol. 42, No. 4, 
April 1972, pp. 163-171. In each of the several sources mentioned above, 
the circuits are unlike those of the present invention. 
DISCLOSURE OF INVENTION 
In keeping with the principles of the present invention, the above and 
other objects are accomplished in a single-port circuit by sensing the 
voltage across the terminals of the port and generating a current in the 
circuit port which is proportional to the impressed voltage. If the 
circuit is comprised of ideal components, then the resulting circuit is 
characterized by an equivalent resistance which obeys Ohm's Law (at least 
over a given frequency range) and has no thermal noise contribution. 
Of course, the non-ideal circuit elements utilized in practical embodiments 
of the present invention result in some thermal noise, although much less 
than that of a passive resistor. By utilizing a field-effect-transistor 
(FET) amplifier the input and output of which respectively sense the port 
voltage and generate the port current, ideal performance is approximated. 
Thus, active circuits operating at room temperatures can be made to 
approximate resistors operating at cryogenic temperatures. 
In keeping with the present invention, embodiments are disclosed which 
utilize dual interconnected and single transformers. Circuits for 
simulating both positive and negative low-noise temperature resistors are 
disclosed. In order to distinguish the positive low-noise simulated 
resistors from conventional resistors, the term "absorbor" has been 
coined, with the ending "or" to conform to the ending in "resistor". 
Similarly, for the negative low-noise resistors, the term "desorbor" is 
employed. In both instances, the "absorbance" and "desorbance" of the 
circuits of the invention have the traditional dimension of ohms.

BEST MODE FOR CARRYING OUT THE INVENTION 
In FIG. 1, there is shown for the purposes of explanation a single-port 
active network which simulates a passive resistor. The circuit of FIG. 1 
comprises an ideal current source 10 and an ideal voltage-responsive 
control signal source 11 connected in parallel between the network 
terminals 1 and 2. (As ideal lossless circuit elements, both control 
signal source 11 and current source 10 are characterized by zero thermal 
noise). Voltage-responsive control signal source 11 generates a control 
signal which is proportional to the voltage E appearing across terminals 
1-2. This control signal, in turn, controls the output of the current 
source 10, which output current I is equal to cE, where c is the constant 
of proportionality. Thus, the current I flowing through the network 
terminals 1-2 is I=cE. 
It is seen that the equation describing the circuit of FIG. 1 is exactly 
the equation for the current flow through an ordinary resistor given by 
Ohm's Law with the conductance G (i.e. 1/R) having been replaced by the 
constant of proportionality c. As mentioned hereinabove, since the network 
of FIG. 1 is assumed to be composed of ideal circuit elements, its noise 
voltage output is zero. From a theoretical standpoint therefore, it is 
seen that it is possible to realize a resistor by means of active circuit 
elements and that the resulting resistor has the property of zero thermal 
noise. 
As a practical matter, of course, it is not possible to realize the circuit 
of FIG. 1 with perfect circuit elements. All practical circuits are 
characterized by finite internal resistances and concomitant thermal 
noise, and in most cases by inherent bandwidth limitations. To the extent 
that the circuits described hereinafter employ non-ideal circuit elements, 
so too will the resulting circuits depart from ideal. Because of the 
particular suitabilities of field-effect-transistors (FETs), the 
embodiments described hereinbelow will be illustrated utilizing FETs as 
the active circuit elements. It is understood, however, that other 
amplifying devices having equally suitable characteristics may be employed 
in many cases. 
Referring more specifically to the schematic diagram of FIG. 2, there is 
shown a two-transformer embodiment of the present invention. In FIG. 2 a 
first transformer 20 having a turns ratio of 1:n is provided with its 
input winding 23 connected to the network terminals 1 and 2. The secondary 
of transformer 20 is connected between the source and gate electrodes of a 
field effect transistor 24 with the source electrode also being connected 
to ground. A second transformer 21 having a turns ratio of m:1 is also 
provided. The primary winding 25 of transformer 21 is connected between a 
source of DC potential V.sub.b and the drain electrode FET 24. The 
secondary winding 26 of transformer 21 is connected in parallel with the 
primary winding of feedback transformer 20 and across the network 
terminals 1 and 2. The DC return path for bias voltage V.sub.b is provided 
by means of the common ground. 
If, as in FIG. 1, the voltage across terminals 1 and 2 of the circuit is 
defined as E, and the circuit current as I, then an analysis of the 
circuit operation of FIG. 2 yields a value for the absorbance, or 
equivalent resistance looking into terminals 1-2 of: 
EQU R.sub.eq =A=1/(g.sub.m nm) [2] 
where g.sub.m is the mutual transconductance of the field effect transistor 
24. From Equation [2] it is seen that by making n equal to 1/m the 
equivalent resistance (absorbance) is equal to the reciprocal of the 
trans-conductance of FET 24. By varying the turns ratio of transformers 20 
and 21 one can obtain a wide range of equivalent resistance values for the 
circuit depicted in FIG. 2. 
In order to analyze the noise contribution, or more accurately, the thermal 
noise contribution of the circuit of FIG. 2, it is convenient to assume an 
open circuit condition at terminals 1-2. It is then found that the 
open-circuit noise voltage can be expressed as: 
EQU e.sub.n.sup.2 =4kT.sub.o BR.sub.n /n.sup.2 [ 3] 
where T.sub.o is the ambivent temperature, and where the noise resistance 
R.sub.n depends upon the particular FET, but for a typical P-channel FET 
is approximately: 
EQU R.sub.n .apprxeq.0.6/g.sub.max. [4] 
Substituting, 
EQU e.sub.n.sup.2 =(4kT.sub.o B/n.sup.2)(0.6/g.sub.max). [5] 
And by operating the circuit, as shown with substantially zero gate bias 
voltage g.sub.m =g.sub.max and from Equation [2], 
EQU e.sub.n.sup.2 =4kT.sub.o B(0.6m/n)A. [6] 
The equivalent noise temperature of the simulated resistor (absorber) of 
FIG. 2 is therefore: 
EQU T.sub.eq =(0.6T.sub.o m/n). [7] 
Thus, the circuit of FIG. 2 simulates a resistor having an absorbance and 
effective temperature which are independently controllable. 
Referring now to the schematic diagram of FIG. 3 there is shown a 
modification of the two-transformer circuit of FIG. 2 which simulates a 
"desorber" or negative resistance. The reference numerals from the 
embodiment of FIG. 2 have been carried over to FIG. 3 to designate like 
circuit elements. The circuit of FIG. 3 is identical to that of FIG. 2 
with the exception that the interconnections to the primary of transformer 
21 have been reversed so that the effective turns ratio is -m:1. As a 
result of this circuit change, the resistance R.sub.eq looking into 
terminals 1-2 is negative and is given by the equation: 
EQU R.sub.eq =A=-(1/g.sub.m nm). [8] 
The output noise character of the negative resistance circuit of FIG. 3 is 
also similar to that given in Equation [6]. Thus, for the embodiment of 
FIG. 3: 
EQU e.sub.n.sup.2 =4kT.sub.o B(0.6m/n) [A]. [9] 
The above equation takes into consideration the noise contribution of FET 
24 but, as before, omits the noise contribution due to the non-ideal 
transformers 20 and 21. It is possible and in some cases perhaps more 
convenient, to reverse the connection to one of the other windings of 
either transformer 20 or 21. The same result can be achieved in this 
manner. That is, a circuit which simulates a negative resistance can be 
obtained by other transformer interconnection reversals. 
Although transformers 20 and 21 have been illustrated as comprising two 
separate cores and their associated windings, in other cases a single 
transformer having but a single pair of windings can be employed with a 
modest sacrifice in circuit operating flexibility. Such a circuit is 
depicted in the schematic diagram of FIG. 4. In FIG. 4 a single 
transformer 40 having a turns ratio of 1:n is connected with its primary 
41 connected through a blocking capacitor 42 to network terminals 1' and 
2'. The secondary winding 42 of transformer 40 is connected between the 
gate and source electrodes of FET 44. The drain electrode of FET 44 is 
connected to the junction formed by the interconnection of primary winding 
41 and blocking capacitor 42. Again, a biasing source shown as V.sub.b is 
provided at the other end of primary winding 41 with the return path being 
provided at the source electrode of FET 44 by means of common ground 
termination. 
The equation for the effective resistance of the one-transformer embodiment 
of FIG. 4 is: 
EQU R.sub.eq =A=1/g.sub.m n . [10] 
And the noise voltage is: 
EQU e.sub.n.sup.2 =4kT.sub.o B(0.6A/n), [11] 
again neglecting the resistance of the transformer windings. 
In applicant's co-pending application Ser. No. 929,582, filed July 31, 
1978, now U.S. Pat. No. 4,180,786, a practical circuit is disclosed for 
impedance matching a signal-generating transducer to a signal-processing 
amplifier while substantially maintaining both the original 
signal-to-noise ratio and original signal amplitudes. Such a circuit is 
shown somewhat simplified, in the schematic diagram of FIG. 5. 
In FIG. 5 a load 50 which can comprise a utilization device such as an 
amplifier, for example, is coupled to a voltage source 51, such as a 
transducer, by means of a section of transmission line 52. The signal 
source 51 is shown as comprising a signal voltage source 53, noise voltage 
source 54 and source impedance 55 connected in series across the input 
terminals of the transmission line 52. At the load end of the circuit, a 
load resistor 56 and its equivalent noise voltage source 57 are serially 
connected together with a negative absorbor circuit 58 across the 
transmission line terminals. In accordance with a preferred mode of 
operation of the circuit of FIG. 5, the value of the load resistance 56 is 
made twice the value of the input resistance and twice the value of the 
characteristic impedance of transmission line 52. That is: 
EQU R.sub.L =2Z.sub.o =2R.sub.s [ 12] 
The negative absorbor 58 provides a negative low-noise resistance of a 
value A which is made equal to the magnitude of the source resistance 
R.sub.S and also to the magnitude of the transmission line characteristic 
impedance Z.sub.o. Expressed mathematically, the value of the negative 
absorbance is: 
EQU A=R.sub.s =Z.sub.o [ 13] 
Summarizing a low-noise resistance can be generally defined as a resistance 
having an associated noise voltage not exceeding approximately 50 percent 
of the noise voltage associated with a conventional (i.e. passive) 
resistor having the same resistance value. An "absorbor" such as depicted 
in FIGS. 2 or 4, uses a power source and a sensing means to create a 
out-of-phase copy of an incoming signal which, when combined with the 
incoming signal, cancels the energy content of the incoming signal. As 
mentioned hereinabove, an absorber emits noise voltages only to the extent 
that it is not perfect. The negative absorbor, or "desorbor" such as that 
shown in FIG. 3, uses a power source and a sensing means to create a 
in-phase copy of an incoming signal, which when combined with the incoming 
signal, increases the energy content of the incoming signal. It is also 
noted that a desorber also emits noise only to the extent that it is not 
perfect. 
With these definitions in mind, the negative absorbor or "desorbor" 58 of 
FIG. 5 can comprise the device of FIG. 3 or one of the devices depicted in 
either applicant's co-pending application Ser. No. 838,511 filed Oct. 3, 
1977 or Ser. No. 881,296, filed Feb. 27, 1978. Examples of specific 
circuits which may be employed for the negative absorber 58 are shown in 
these applications. For the purposes of discussion however, it is assumed 
that negative absorbor 58 comprises the circuit shown hereinabove in FIG. 
3. It is assumed that negative absorbor 58 generates a small noise voltage 
compared to that of a noise source 57 associated with load resistor 
R.sub.L. When this assumption is made, the impedance Z.sub.L of the 
overall load portion of FIG. 5 is given by: 
EQU Z.sub.L =R.sub.L -A. [14] 
Substituting Equations [12] and [13] into Equation [14] yields: 
EQU Z.sub.L =2Z.sub.o -Z.sub.o =Z.sub.o 
Thus the impedance seen by transmission line section 52 is equal to its 
characteristic impedance and therefore, the transmission line is properly 
terminated with a matched load. 
In the above mentioned co-pending application Ser. No. 929,582 it is also 
shown that the signal voltage across the input to load 50 under the 
conditions described above is equal to S. That is, the signal voltage at 
the input to the load is undiminished in amplitude from the original 
signal voltage S. 
In the circuit of FIG. 5 there are three sources of noise to consider, 
namely, that of the signal source 51 represented by noise source 54, the 
load resistor 56 represented by noise voltage source 57 and that of the 
negative absorbor 58. The noise voltage appearing at the input to load 50 
can be expressed as: 
##EQU1## 
Thus, all of the noise voltage V.sub.s of signal source 51 appears at the 
input to load 50. It can also be shown that the noise voltage due to 
negative absorbor 58 also appears at the input to load 50; however, the 
noise of load resistor 56 represented by noise source 57 does not appear 
at all. The voltage V.sub.L of the load resistor noise source 57 is 
exactly cancelled by the voltage appearing across load resistor 56 due to 
the noise current from the noise source 54. These relationships again, are 
derived in the above mentioned co-pending application, and for the sake of 
simplicity, are not duplicated herein. 
When these factors are taken into consideration the circuit of FIG. 5 can 
be redrawn as shown in FIG. 6. The resulting circuit comprises a load 50 
represented by a dashed box and an equivalent load resistor 56. Feeding 
load resistor 56 is the serial combination of the signal voltage source S, 
its input resistance R.sub.s and the negative absorbor 58. If, as 
postulated, the magnitude of the input resistor 55 and the absorbor 58 are 
equal and opposite, then the circuit further reduces to a signal source of 
diminishingly small internal impedance feeding the load resistance 56. The 
signal voltage source 53 is, in its ideal case a signal generator of very 
low impedance (its impedance having been represented by R.sub.S). Thus, it 
is seen that the entire signal voltage S is applied across the load 
resistor R.sub.L, while the very low impedance of the signal voltage 
source 53 effectively short-circuits the load resistor thereby effectively 
short-circuiting the voltage noise of the resistor V.sub.L. 
It is seen then that the circuit of FIG. 5 and its simplified equivalent of 
FIG. 6 not only provides a matched load to its signal source 51 and the 
transmission line 52 and does this with minimum degradation of the 
signal-to-noise power ratio, but it also transmits the signal voltage to 
the load undiminished in amplitude. 
In all cases, it is understood that the above-described embodiments are 
merely illustrative of but a small number of the many specific embodiments 
which can represent applications of the principles of the present 
invention. Numerous and various other arrangements can be readily devised 
in accordance with these principles by those skilled in the art without 
departing from the spirit and scope of the present invention.