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Description  |
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FIELD OF THE INVENTION
The present invention relates to a low distortion amplifier circuit of the
predistortion type. More particularly, it relates to an amplifier circuit
particularly useful for amplifying a multi-tone input signal, and which
uses a cuber circuit to provide third order distortion energy that cancels
corresponding energy in a main power amplifier, so as to provide a
distortion free output.
BACKGROUND OF THE INVENTION
When a multi-tone signal is amplified, as is the case in a wide variety of
applications, undesirable intermodulation distortion (IMD) products are
inherently produced, resulting in distortion of the amplified output
signal. These IMD products are particularly troublesome in wireless
communications applications where signals of several frequency channels
are often amplified by a common amplifier. Without proper reduction of the
IMD products, signal interference between adjacent channels or within a
single channel can become excessively high.
In order to achieve low intermodulation distortion, the amplifier typically
has to be backed off from its thermally rated average power output and
linearized. In wireless applications, both of these approaches add
significantly to the high cost of the transmitting amplifier.
RF amplifiers have been linearized in the past via the use of either
predistortion or feed-forward methods of canceling intermodulation. Feed
forward amplifier circuits typically employ a main amplifier which
produces fundamental and unwanted IMD power, along with a correction
amplifier to produce only IMD power. The IMD power of the two amplifiers
are then cancelled in an output combiner. While this feed-forward
technique is satisfactory for some systems, it is very expensive and
requires critical alignment. An example of a feed-forward, low distortion
amplifier can be found in U.S. Pat. No. 5,304,945 entitled "Low-Distortion
Feed-Forward Amplifier", which is assigned to the assignee herein.
Predistortion methods to reduce IMD have also been utilized in the prior
art. In a predistortion amplifier circuit, the input signal is split into
two paths: a direct path and a predistorter path. In the predistorter
path, the input signal is conditioned in some manner to produce a
predistorter signal that contains some signal energy at IMD frequencies.
This predistortion signal is then combined with the signal in the direct
path, and the combined signal applied to a main amplifier. The output
signal of the main amplifier then will have less distortion than it would
without the predistorter signal, provided that the amplitude and phase of
the predistorter signal is properly selected.
An example of a prior art predistortion amplifier can be found in U.S. Pat.
No. 4,157,508 entitled "Signal Cuber Circuit". The amplifier circuit in
this patent utilizes a pair of anti-parallel diodes in the predistorter
path to generate signal energy at the IMD frequencies. This diode
arrangement creates a "cuber"--i.e., a circuit which produces signals at
the third order IMD frequencies. The cuber disclosed therein used a
balance bridge to minimize the signal leak-through at the fundamental
frequencies, and an additional resistor to minimize the 5th order
distortion in the cuber output. However, for signal-to-noise (SNR)
considerations, diodes with large reverse saturation current had to be
used, with associated large junction capacitance. This choice limited the
frequency response of the diodes, thus preventing that cuber's use at high
frequencies such as in standard cellular telephone bands.
SUMMARY OF THE INVENTION
In one embodiment of the present invention, a low distortion amplifier
circuit of the predistortion type employs a cuber circuit in a
predistortion path to provide optimized signal energy at third order
intermodulation frequencies, which cancels IMD products generated by the
main power amplifier. The cuber circuit employs a pair of anti-parallel
diodes that are biased with at least one D.C. source to produce a D.C.
current flow through each diode. The input signal applied to the cuber
circuit produces signal current flow in each diode to enable a third order
output current to be extracted via a load impedance. A desired amount of
third order power is thereby provided to realize minimal IMD power in the
main amplifier output signal, over a wide dynamic range of the input
signal.
Using a circuit analysis based on a power series approximation, circuit
parameters of the cuber circuit can be optimized to provide a desired
amount of cancellation of third order IMD products in the main amplifier,
without generating excessive higher order power, over an optimized dynamic
range of the input signal.
Preferably, a variable gain low noise amplifier (LNA) is employed in the
predistorter path following the cuber circuit to further optimize the
third order predistortion power level. A correction feedback loop may then
be employed to detect the unwanted IMD power in the main amplifier output
signal, to control the LNA gain in accordance with the IMD power detected.
Optionally, the feedback loop uses a dither tone generator in conjunction
with a multiplier, an integrator and a summing circuit to provide
continuous adjustment.
BRIEF DESCRIPTION OF THE FIGURES
For a full understanding of the present invention, reference is had to an
exemplary embodiment thereof, considered in conjunction with the
accompanying drawings wherein like reference numerals depict like
features, for which:
FIG. 1 shows an embodiment of a low distortion amplifier circuit of the
present invention;
FIG. 2 is representation of an ideal anti-parallel diode configuration;
FIG. 3 shows an embodiment of a cuber circuit which can be used within a
low distortion amplifier circuit of the present invention;
FIG. 4 illustrates noise sources within the cuber circuit of FIG. 3;
FIG. 5 depicts graphs of dynamic range as a function of resistances within
the circuit of FIG. 3;
FIG. 6 shows graphs of the magnitude of various frequency components of the
cuber circuit output as a function of input voltage;
FIG. 7 is a graph of the cuber circuit dynamic range as a function of bias
current;
FIG. 8 shows graphs which compare predicted and measured results for a
cuber circuit of the present invention;
FIG. 9 is an embodiment of a UHF cuber circuit according to the present
invention;
FIG. 10 shows graphs which compare predicted and measured results for a UHF
cuber circuit; and
FIG. 11 depicts an alternate embodiment of a low distortion amplifier
circuit of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, there is shown a predistortion power amplifier circuit
10 according to one embodiment of the present invention. By way of
illustration, the operation of circuit 10 will be described hereafter in
reference to the low distortion amplification of a two tone input signal
S.sub.in with high frequency, sinusoidal tones at frequencies f1 and f2.
It is understood, however, that low distortion amplification of multi-tone
input signals having more than two tones can also be accomplished with
amplifier circuit 10.
Amplifier circuit 10 includes power amplifier 20 functioning to produce
high RF power at fundamental frequencies f1 and f2, which may lie in the
UHF frequency band, for example. Frequencies f1 and f2 are assumed to be
at fc-.gamma. and fc+.gamma., respectively, where fc is a reference
carrier frequency. Now, if signal S.sub.in were to be applied directly to
the input port of power amplifier 20, the output of amplifier 20 would
consist of amplified fundamental power at frequencies f1 and f2, as well
as undesirable distortion frequency power at third order intermodulation
distortion (IMD) frequencies f3 and f4, where f3=fc-3.gamma. and
f4=fc+3.gamma.. With the present embodiment, these intermodulation
products are substantially reduced by employing cuber circuit 14, which
produces an optimum amount of power at distortion frequencies f3 and f4.
This power will essentially cancel the power at f3 and f4 inherently
produced by power amplifier 20 to produce a distortion free output signal
S.sub.out.
Briefly, input signal S.sub.in is split by means of coupler 12 to produce a
direct path output signal that is applied to delay line 13, and a coupled
path output applied to cuber 14. Cuber 14 produces output signal S1
containing components at frequencies f1-f4 with the amplitude of each
frequency component optimized. Signal S1 also contains some undesirable
power at the fifth order IM frequencies f5=fc-5.gamma. and f6=fc+5.gamma.
and at higher order frequencies as well. A highly linear, variable low
noise amplifier (LNA) 16 amplifies signal S1 to adjust the amplitude of
the cuber output.
Variable phase shifter 17 is utilized to phase shift the output of LNA 16
to provide signal S2 that is applied to one input port of summer 18. The
output of delay line 13 is applied to the other input port of summer 18.
The primary function of delay line 13 is to match the delay, at
frequencies f1 and f2, of the components in the predistortion path--that
is, cuber 14, LNA 16 and interconnecting transmission lines (but not the
desired phase shift of phase shifter 17). By proper selection of the delay
line 13 electrical length and of the phase shifter 17 phase shift, summer
output signal S3 can be provided with the phase of the fundamental and
distortion frequencies independently controlled. For instance, if an
unequal power splitting Wilkinson type combiner is used for summer 18, and
the f1 and 12 components of signal S2 are 180.degree. out of phase with
those of the delay line 13 output signal, then the f1 and 12 components of
signal S3 will be the delay line 13 output signal minus signal S2, at an
arbitrary phase of .THETA.f degrees. In this case, the f3 and f4
components of signal S2 will be at an arbitrary phase of .THETA.d degrees.
If the delay line 13 electrical length changes, the magnitude of the f1
and f2 components of signal S3 will be increased because a pure
subtraction no longer occurs and the phase will differ from .THETA.f.
Meanwhile, the phase of the f3 and f4 components of signal S3 remains at
.THETA.d. Accordingly, the absolute phase of the f1 and f2 components of
signal S3 may be independently controlled relative to the absolute phase
of the f3 and f4 components of signal S3. This independent phase control
will enable cancellation of the distortion frequencies within power
amplifier 20, provided that the amplitude of the distortion components of
signal S3 is properly set. Accordingly, the AM to PM conversion in the
amplifier 20 can be compensated for. For instance, if amplifier 20 has a
voltage gain of G1 and the f3 and f4 components of signal S3 are each of a
magnitude A3, then these components will be amplified and appear as
components of the S.sub.out signal, each with amplitudes of A3G1.
Meanwhile, the f1 and f2 components of signal S3 are amplified and
produce, as part of the S.sub.out signal, IMD products at f3 and f4, each
with amplitude B3. Hence, if the S.sub.out distortion components with
magnitude A3G1 is 180.degree. out of phase with the S.sub.out distortion
products with magnitude B3, then all distortion frequency output power of
S.sub.out will be eliminated if A3G1=B3. The present embodiment is
operative to provide this desirable result.
One practical limitation with this embodiment is the presence of fifth
order distortion components in the S.sub.out signal at frequencies
f5=fc-5.gamma. and f6=fc+5.gamma.. This fifth order distortion consists of
three parts: 1) the original fifth order distortion created by power
amplifier 20 due only to the amplification of the f1 and f2 components of
signal S3; 2) fifth order components of signal S2 due to imperfections in
cuber circuit 14; and 3) fifth order distortion produced in power
amplifier 20 due to the interaction between the f1, f2 components and f3,
f4 components of the S3 signal as they are amplified. Since power
amplifier 20 will operate in a more linear region than cuber circuit 14,
item (2) above would be the dominant part among the 5th order terms. It is
therefore important for the cuber to produce minimal 5th order residue.
The cubic response of cuber circuit 14--i.e., the ability to produce third
order intermodulation power (at frequencies fc+3.gamma. and
fc-3.gamma.)--is derived from the non-linear response of semiconductor
diodes employed therein.
To provide a foundation for the detailed operation of the embodiments of
cuber circuit 14 to be described subsequently, reference is first had to a
simplified anti-parallel diode cubic predistorter 22 as shown in FIG. 2. A
pair of identical anti-parallel diodes D1 and D2 are driven by a time
varying input voltage "v" produced by a voltage source 24. Each diode
D1,D2 has the following voltage-current relationship:
i.sub.D =I.sub.0 (e.sup..beta.v -1), (1)
where v is the voltage across the diode, .beta. is typically 40
volts.sup.-1, I.sub.0 is the reverse saturation current of each diode, and
i.sub.D is the current flowing through each diode (i.sub.D =i.sub.1 and
i.sub.2 for diodes D1 and D2, respectively). The combined current flow of
the identical antiparallel diodes is,
i=i.sub.1 -i.sub.2 =I.sub.0 (e.sup..beta.v -e.sup.-.beta.v).(2)
Thus,
##EQU1##
If voltage is derived by passing i through a low value resistor (not shown)
of less than about 1.OMEGA., an output voltage can be obtained which
consists of first, third and fifth order terms of the input voltage. The
first order term can be cancelled by proper combining with the input
voltage. The 5th order term can be made arbitrarily small by controlling
the value of .beta.v to be much less than unity. What remains, then, is
essentially a 3rd order term.
A typical high frequency diode has an I.sub.0 current of about 20 nA, which
implies a high conversion loss between the input and output signals.
Therefore, thermal noise would overwhelm the output power, unless the
circuit is operated at a large .beta.v value; however, the latter would
cause the higher order distortions to dominate the cubic distortion.
Secondly, to avoid excessive conversion loss, a larger resistor is needed
for the output voltage. It is noted that a large resistor in circuit 22
would change the ideal voltage-current formula of equation (2).
Referring now to FIG. 3, there is shown one embodiment of cuber circuit 14
which can be used in circuit 10 of FIG. 1. A pair of packaged diodes D3
and D4 include ideal diodes D1 and D2, respectively, with each ideal diode
in series with a bulk resistance R.sub.b. This bulk resistance R.sub.b is
associated with every commercially available diode and is typically on the
order of 10-20 ohms. A pair of DC sources 30 each supply a DC bias voltage
V.sub.b in a series path with each diode D3 and D4. The introduction of
bias voltage V.sub.b produces a bias current, I.sub.b, which is many
orders of magnitude larger than I.sub.0. The current I.sub.b is added with
the currents i1 and i2 that would otherwise flow through respective ideal
diodes D1 and D2, so that the current i1+I.sub.b now flows through diode
D3, and current i.sub.2 +I.sub.b flows through diode D4.
Replacing voltage source 24 of the ideal circuit of FIG. 2 is the series
combination of a voltage source 26 that produces a time varying input
voltage V.sub.i, a source impedance R.sub.s and a load impedance R.sub.L.
Load impedance R.sub.L is essentially the input impedance of amplifier 16
of FIG. 1. If an impedance transformer is utilized between cuber circuit
14 and amplifier 16, R.sub.L will be the impedance "looking into" the
transformer/amplifier arrangement. Load resistance R.sub.L is introduced
to derive meaningful power to combat subsequent amplifier noise.
The voltage V.sub.i represents the superimposed, multi-tone sinusoidal
voltages supplied to cuber 14 from the coupled output path of coupler 12.
Source impedance R.sub.s is the impedance "looking back" towards
directional coupler 12 from cuber input port 15. Typically, characteristic
impedance Zo of coupler 12 is 50.OMEGA.; however it is desirable to
transform the 50.OMEGA. impedance to a much lower impedance on the order
of one ohm. Hence, impedance R.sub.s will be the lower transformed
impedance. The transformation may be realized at higher frequencies with
the use of a multi-stepped microstrip transformer (not shown) between
coupler 12 and cuber circuit 14 with each step being a quarter wavelength
long so that the 50.OMEGA. impedance is transformed in several steps down
to the much lower impedance R.sub.s. Such multi-stepped transformers are
well known in the art and generally utilized to transform impedances over
narrow to medium range bandwidths. At lower frequencies, a lumped element
transformer would be used.
This embodiment uses optimized values for the parameters R.sub.b, R.sub.s,
R.sub.L, and V.sub.b, which are selected to arrive at cuber circuit 14,
which can operate over an optimized dynamic range of V.sub.i. The
mathematical power series based analysis set forth below, enables one
skilled in the art to select the above-noted parameters so that a desired
cuber circuit output power at the third order frequencies is obtained
while output power at fifth and higher order frequencies is minimized. The
lower end of the dynamic range will be shown to be limited by the noise
within the circuit; the higher end is limited by the eventual dominance of
the fifth and higher order power over the third order power.
I. Circuit Analysis Using Power Series Expansion
At the outset, the input voltage V.sub.i will produce a voltage "V" across
the nodes 32 and 34 according to the equation:
V=V.sub.i -iR, (4)
where R=R.sub.s +R.sub.L. Also,
I.sub.b =I.sub.0 (e.sup..beta.(v.sbsp.b.sup.-I.sbsp.b.sup.R.sbsp.b.sup.)
-1). (5)
A voltage V.sub.d1 will appear across the diode D1 as:
V.sub.d1 =V-i.sub.1 R.sub.b +V.sub.b -I.sub.b R.sub.b. (6)
Therefore,
i.sub.1 +I.sub.b =I.sub.0 (e.sup..beta.V.sbsp.d1 -1)=(I.sub.b
+I.sub.0)e.sup..beta.(V-i.sbsp.1.sup.R.sbsp.b.sup.) -I.sub.0,(7)
or,
i.sub.1 =I.sub.s e.sup..beta.(V-i.sbsp.1.sup.R.sbsp.b.sup.) -I.sub.s,(8)
where I.sub.s .tbd.I.sub.b +I.sub.0. Similarly, we obtain,
i.sub.2 =I.sub.s e.sup.-.beta.(V+i.sbsp.2.sup.R.sbsp.b.sup.) -I.sub.s,(9)
and,
i=i.sub.1 -i.sub.2 =I.sub.s [e.sup..beta.(V-i.sbsp.1.sup.R.sbsp.b.sup.)
-e.sup.-.beta.(V+i.sbsp.2.sup.R.sbsp.b.sup.) ]. (10)
From the symmetry of the circuit, it can be shown that
i(V)=-i(-V) and i(V.sub.i)=-i(-V.sub.i). (11)
Since i is an odd function of V.sub.i, it should be expressible as an odd
series of V.sub.i, to wit,
##EQU2##
Equation (8) can first be solved for V as a power series expansion in
i.sub.1 /I.sub.s :
##EQU3##
where .xi. is defined as:
.xi..tbd.1+I.sub.s .beta.R.sub.b. (14)
Using the power series reversion formula--as disclosed by M. Abramowitz and
I. A. Stegun, Eds., "Handbook of Mathematical Functions", National Bureau
of Standards, Applied Mathematics Series #55, 3rd Printing, March 1965,
page 16, Eq. (3.6.25)--gives i.sub.1 /I.sub.s as a power series in
.beta.V:
##EQU4##
Similarly the power series for i.sub.2 /I.sub.s is found as:
##EQU5##
Combining Equations (15) and (16) gives,
##EQU6##
Again applying series reversion, V expanded in powers of i is,
##EQU7##
Combining Equations (4) and (18) gives a power series for V.sub.i in terms
of i,
##EQU8##
where .eta. is defined as:
.eta..tbd.1+I.sub.s .beta.(R.sub.b +2R). (20)
Using series reversion again, one can obtain the desired power series of i
in terms of V.sub.i, Equation (12), where the coefficients are given by:
##EQU9##
It is noted that, for a given bias voltage V.sub.b, the output voltage
across R.sub.L is completely defined by iR.sub.L, where i is given by
##EQU10##
and the C's are defined by Equations (21)-(24). It is also noted that
C.sub.5, i.e., the 5th order distortion, can be reduced by adjusting R,
for any fixed bias current.
II. Two Tone Case
A convenient method of measuring the performance of cuber circuit 14 is to
use a time varying input voltage V.sub.i consisting of two sine waves of
different frequencies fc+.gamma. and fc-.gamma. as mentioned previously.
It is understood, however, that cuber circuit 14 can also be used to
generate third order output when V.sub.i is made up of more than two
sinusoidal tones. (Moreover, it is noted that cuber circuit 14 can also be
used to generate third harmonic power for a single tone input, to cancel
or tailor third harmonic power generated in the main power amplifier. This
would be desirable in some microwave amplifiers to increase efficiency by
shaping voltage and current waveforms using harmonic power.)
For the two-tone input, V.sub.i is defined as:
V.sub.i =acos (.omega..sub.c t+.delta.t)+acos (.omega..sub.c t-.delta.t)=2
acos (.delta.t) cos (.omega..sub.c t), (25)
where .omega..sub.c =2.pi.fc and .delta.=290 .gamma.. Inserting Equation
(25) into Equation (12) and retaining only terms in the band centered on
the radian carrier frequency, .omega..sub.c, a current i.sub.f flowing
through R.sub.L in the fundamental frequency band, can be found as:
##EQU11##
Accordingly, by proper selection of the parameters C.sub.1, C.sub.3,
C.sub.5 and C.sub.7, which are in turn functions of the circuit parameters
of FIG. 3 described hereinabove, a desired third order output power can be
realized while power at the other frequencies is controlled.
III. Dynamic Range Considerations
Since the purpose of cuber circuit 14 is to provide a third order output
that can be used to cancel the third order power generated in power
amplifier 20, the fifth and higher order distortion from cuber 14 are
undesirable, unless they can be controlled to cancel similar terms in the
power amplifier. Thus, for example, if it is desired to cancel the third
order distortion by 30 dB, the high power limit of the cuber predistorter
arrangement occurs when the input power to cuber 14 is high enough to make
the fifth and higher order distortion equal to 0.1% (i.e., -30 dB) of the
third order output of the cuber. Allowing the input power to rise above
this point would begin to defeat the purpose of the cuber circuit
arrangement of canceling third order distortion output, since higher order
distortion output would begin to rise to unacceptably higher levels. A
simple way to ensure dominance of the third order relative to the higher
order distortion, is to attenuate the input signal to cuber 14 and amplify
its output using variable amplifier 16 before coupling to the input of
power amplifier 20. The difficulty with this approach is that the third
order cuber output becomes comparable to its noise output. Thus the
dynamic range of cuber 14 is determined by the range of input power
between the lowest input power level--that is, the level where its third
order output power is comparable to its noise output--and the highest
input power level, which is where the higher order distortion becomes
comparable to the third order output. These dynamic range limits are based
on the assumption that the fundamental (linear) leak-through power of
cuber 14 at frequencies fc+.gamma. and fc-.gamma., is prevented from
becoming so large that it significantly reduces the signal input to power
amplifier 20 when the cuber output is coupled to the power amplifier
input, thereby reducing the gain of the power amplifier to the extent that
it must be redesigned. (This fundamental power is part of signal S2 of
FIG. 1 which is generally subtracted from the output signal of delay line
13 by summer 18).
An important parameter in estimating the cuber noise output is its
bandwidth. For example, in wireless communication applications, it is
desirable to cancel the intermodulation in a radio channel to be 60 dB
below the carrier level that is normally used for radio transmission in
that channel (-60 dBc). At the low power limit of operation, the
intermodulation of the power amplifier should just be rising above the -60
dBc level, so it would be desirable for the noise in the channel bandwidth
to be about 10 dB less (-70 dBc). To compare this with the third order
output of cuber 14, it is necessary to specify the number of channels, M,
transmitted. The third order output per channel is approximately 1/Mth of
the total intermodulation output. Thus, the low power end of the dynamic
range of cuber 14 is the point where the noise power output per channel
bandwidth is about 10 Log.sub.10 (10M) dB below the third order output.
Since the upper limit of the dynamic range is roughly independent of the
number of channels, it is seen that the dynamic range is reduced as the
number of channels increases.
As shown in FIG. 4, the noise sources of cuber 14 consist of shot noise
I.sub.shot-1, I.sub.shot-2 in the respective diodes D1, D2; the resistor
thermal noises e.sub.Rb, e.sub.RS ; and the noise introduced by low noise
amplifier 16. To facilitate the following approximate noise analysis, it
is noted that in order to maintain non-linear operation, the effective
resistance of the diode junctions are biased, by means of D.C. sources 30,
to be much larger than resistances R.sub.s, R.sub.b and R.sub.L. The load
resistance R.sub.L in FIG. 4 is shown to consist of the impedance looking
into a transformer 34 in front of the LNA 16.
The mean square shot noise current of a diode is given by:
I.sup.2.sub.shot =2qIB, (27)
where q is the electronic charge, 1.602(10.sup.-19) coulombs, I is the
current through the diode, and B is the bandwidth of the input signal,
typically 30 KHz per channel in wireless applications. Noise is of
interest because it limits the low power range of operation of cuber 14,
where the signal currents, i.sub.1 and i.sub.2 are small. Therefore, the
contribution of i.sub.1 and i.sub.2 to the current I can be neglected and
I can be approximated by the D.C. bias current I.sub.b in each of the
diodes. Since diode junction resistance is much larger than R.sub.s and
R.sub.L, approximately all shot noise currents pass through R.sub.L via
the input source. Therefore, the mean square shot noise current passing
through R.sub.L is
i.sup.2.sub.shot .congruent.4qI.sub.b B, (28)
Similarly, the total mean square noise current passing through R.sub.L due
to the two bulk resistors R.sub.b is:
i.sup.2.sub.nb .congruent.8kTBR.sub.b (.beta.I.sub.s).sup.2,(29)
where only the linear term in Equation (15) is used and .beta.I.sub.s
R.sub.b is neglected relative to unity (which implies the small signal
conductance of the diode junction is .beta.I.sub.s mhos). In Equation (29)
the term 8kTBR.sub.b results from the mean square thermal noise voltage of
resistor R.sub.b, where Boltzmann's constant k=1.38.times.10.sup.-23
/Joules/K and, at room temperature, T=293.15K. Approximating .eta. unity
in Equation (21), the mean square noise current through R.sub.L due to the
source resistance, R.sub.s is
i.sup.2.sub.ns .congruent.(2.beta.I.sub.s).sup.2 4kTBR.sub.s.(30)
As shown in FIG. 4, the noise of amplifier 16 is represented by equivalent
input noise voltage e.sub.na and current I.sub.na generators which can
typically be assumed to be uncorrelated. The ratio of their magnitude is
called the noise resistance, R.sub.n .tbd..sup.e.sbsp.na /.sub.i.sbsb.na.
The noise resistance R.sub.n of amplifier 16 can be measured by comparing
its output noise when the amplifier input is open circuited, "N.sub.oc "
to that when the amplifier input is short circuited, "N.sub.sc ", as
follows:
##EQU12##
Then, in terms of amplifier 16 noise figure, F, e.sup.2.sub.na is defined
as
##EQU13##
Typically, N.sub.oc >>N.sub.sc, so that the amplifier equivalent input
noise current I.sub.na dominates over its equivalent input noise voltage
e.sub.na and R.sub.n is small compared to unity. The mean square noise
current through R.sub.L due to e.sub.na is, using the same approximation
for C.sub.1 as in Equation (28),
##EQU14##
As in Equation (26), it is assumed that the small signal junction
resistance of the diodes is large compared to R.sub.L, so that most of
i.sub.na flows through R.sub.L :
##EQU15##
The total mean square noise current i.sup.2.sub.nt through R.sub.L is thus
the sum of that given in Equations (28)-(30), and (32)-(34),
##EQU16##
It will be shown in later examples that the equivalent input noise current
of LNA 16 is the dominant noise source so that the total mean square noise
current may usually be approximated by
i.sup.2.sub.nt .congruent.4kTB(F-1)R.sub.L. (36)
Since LNA 16 is usually needed to set the level of the third order
predistortion to be coupled into the input of power amplifier 20, it
cannot be deleted in most practical applications to avoid the major noise
source.
To arrive at a minimum usable input voltage V.sub.imin, it is assumed that
the cuber output signal flowing through R.sub.L is the third order current
i.sub.S3 in Eqn. (12), that is:
##EQU17##
where A(t) and .THETA.(t) are the slowly varying (with respect to the
radian carrier frequency, .omega..sub.c) envelope and phase, respectively,
of the narrowband representation of the input signal. Thus, the
fundamental-band, mean square, third order current through R.sub.L is:
##EQU18##
where the brackets, <>, imply the average value of the argument, and the
second approximation in Equation (37) assumes .xi.=.eta.=1, as in Equation
(36).
It can then be determined that the minimum usable input voltage V.sub.imin
is applied when
i.sup.2.sub.S3 .congruent.XMi.sup.2.sub.nt, (39)
where X is the power amplifier intermodulation level, relative to the
channel bandwidth noise level--e.g., 10 dB in the above example.
Accordingly, using the above noise analysis, one can arrive at the lower
end of the dynamic range of cuber circuit 14, as a function of variables
such as targeted intermodulation output level (-60 dBc in the above
example), channel bandwidth B, LNA 16 noise figure F, and load resistance
R.sub.L.
IV. Determining Maximum Input Level
Having thus formulated a criteria for arriving at the minimum input voltage
V.sub.imin to cuber circuit 14, guidelines for determining a maximum input
voltage, V.sub.imax will now be presented. A determination of V.sub.imax
will then establish the dynamic range of cuber circuit 14.
Referring again to Equation (39), V.sub.imin is defined as the input
voltage which yields a 3rd order output mean square current which is X
times stronger than the mean square noise current (primarily the output
amplifier 16 noise) on a per-channel basis. With X=10 as an illustrative
case, Eqns. (35), (38) and (39) give,
##EQU19##
The maximum cuber circuit input voltage, V.sub.imax, is defined hereafter
as the input voltage which produces 5th or 7th order output voltages that
are within "Y" dB of the 3rd order output, where Y represent the amount of
3rd order power cancellation which is desired in power amplifier 20. An
exemplary value for Y is 30 dB (or 1,000). With V.sub.i =V.sub.imax, Eqn.
(12) yields:
##EQU20##
The decibel difference between V.sub.imax and V.sub.imin is defined as the
dynamic range: 20 Log.sub.10 (V.sub.imax)/V.sub.imin). The exemplary -30
dB limit (i.e., Y=1,000) on the higher than 3rd order distortions is an
arbitrary choice based on the assumption that the predistorter arrangement
will be used to cancel the 3rd order intermodulation of power amplifier 20
by about 30 dB, at which point the 5th or 7th order distortion can become
major contributors to overall distortion if they exceed -30 dB relative to
the 3rd order predistorter output. Other choices for "Y" can be made if so
desired; however, they would have only a small effect on the dynamic range
(because of the rapid increase of the 5th and 7th order distortion at the
high input power), and furthermore parameter optimization is only slightly
affected by the particular choice of dynamic range.
The following qualitative comparisons for a) V.sub.imax range; b) circuit
resistances; and c) bias current, were obtained assuming diodes with the
characteristics: I.sub.0 =2 nA, R.sub.b =13 Ohms, and .beta.=38.686/volt.
For noise calculations, it is assumed that MB=1 MHz (e.g., 40 channels
with 25 kHz bandwidth); LNA 16 noise figure of 6 dB (F=4.0); and a zero
equivalent noise resistance (R.sub.n =0).
To determine an exemplary range of V.sub.imax, it is first noted that most
of the input voltage appears across diodes D1 and D2. Since the
fundamental nonlinearity is exp(.beta.V.sub.i), the higher order harmonics
become significant after .beta.V.sub.i is greater than unity. Experimental
results have indicated that, in order to keep the 5th and 7th order terms
30 dB below the 3rd order term, .beta.V.sub.imax is in the range of 2 to
3, or V.sub.imax is about 50 to 75 mV--a result which is fairly
independent of the bias current or the total resistance in the circuit.
As for the resistance in the circuit--the load resistance R.sub.L has an
impact on the output power and also on the relative strength of the power
series coefficients, {C.sub.i }. In order to emphasize the similarity of
the dependence of dynamic range on circuit resistance for vari | | |
