Post-Distortion Linearising Technique Applied to Mixers
João P. Martins, Nuno Borges Carvalho, José Carlos Pedro
Instituto de Telecomunicações, Campo Universitário, 3810-193 Aveiro, Portugal
joaoptm@av.it.pt; nborges@ieee.org; jcpedro@ieee.org
Abstract
This paper presents a new approach for the mixer
linearization based on the post-distortion technique. A two
tone simulation was performed at frequencies of 1.8 GHz
with a separation of 200 KHz. The validity of the technique is
verified by simulation.
I. INTRODUCTION
A mixer is a nonlinear device that can be found in almost all
telecommunication equipment. It plays a very important role
performing the translation from RF to the IF (downconversion) and vice-versa.
Since a mixer is inherently nonlinear in order to achieve
mixing, its distortion behaviour is a matter of concern.
One way to minimize the nonlinear distortion is to use
external linearizing devices.
In the design process, there are some techniques that can be
used in order to achieve a favourable behaviour concerning
linearity. Nevertheless, when operating near the compression
point, spectral regrowth is always present.
In wide band communication systems scenario, every
carrier, in the presence of system nonlinearity, behaves like a
jammer to the adjacent channels. The global multi-carrier
signal’s behaviour could only be predicted statistically and
the peak power may be much higher than the average signal
level.
Then, operating a mixer at lower input power values is not a
solution due to the extended dynamic range of the signal. One
way out is to decrease the noise’s device and, as a
consequence, improve the SNR (Signal to noise ratio). But,
higher earns could be achieved by expanding the operating
area towards the compression zone.
A lot of research has been done until now and mixers
became a well understood and performing device, fulfilling
the demands of the underlying applications. However, the
new advent of the wireless world is reformulating the
telecommunications standards, and the way people conceive
solutions is no longer the same. In this sense, the scientific
community has been challenged in the way of improving
electronic device’s behaviour where mixers are included, so
that the final solutions have a higher performance and a
competitive cost.
Some topologies had been proposed to solve the linearity
problem of mixer at the system level. Figure 1 presents a
topology based on the feed-forward technique [2].
Fig 1- Diagram of the mixer feed-forward lineariser.
This approach is composed by two equal mixer devices
placed in independent branches. The RF signal is applied to
both mixers but at different power levels. This is achieved by
splitting the RF signal in two branches and attenuating one of
them. The upper mixer is the principal one, operating with a
strong input, therefore it distorts the signal, and spectral
regrowth is noticed. The mixer in the lower branch is
operating in back-off mode and it distorts the signal very
slightly.
The IF signal is then amplified and adjusted in opposite
phase to the signal of the top branch. Both signals are added
and if the system is finely tuned, the IMD generated by the
top branch cancels the IMD in the lower branch and the result
is an output signal without distortion.
In practical realizations the results are not so promising due
to the precision required in the amplitude and phase of the
signals to be added. The level of IMD rejection reported in
[2] is near 20 dB. The critical points in this approach are the
amplifier’s distortion which is not cancelled and passes
directly to the output, and the low dynamic range caused by
the sensitivity to the IMD’s amplitude changes.
Other approach is based on the pre-distortion technique
which is the most spread linearsing method in the industry.
The main reasons are its simplicity and fair results.
Fig 2- Diagram of the pre-distortion lineariser.
Figure 2 shows the basic topology and the signal spectrum
in each point of the circuit. The main idea in this point is to
change the input signal in the way that the result of its
conversion is a signal without distortion. So, it is necessary to
characterize the mixer’s behaviour in terms of distortion.
Then, before applying the signal to the mixer, it is required
that it passes trough a device that has an inverse IMD
characteristic in relation to the mixer.
This characteristic corresponds to a gain expansion. The
way to achieve such a characteristic is to subtract a nonlinear
device operated at compression from other with a linear
behaviour. The resultant signal has to be adjusted in phase
and amplitude, with a vector modulator, Fig. 2, to match the
opposite characteristic of the mixer.
The results reported for the IMD cancellation in this setup
are close to 15 dB [4]. The complete system’s conversion loss
rate increases in relation to the single mixer due to the
contribution of the pre-distorter.
The main disadvantage of this setup is the deviation from
the tuning point due to the aging process and changes in
devices’ temperature. This is a critical point since this
configuration works in open loop, so, no feedback is
provided.
Another setup now using a feed-back topology is presented
in the Fig 3.
The proposed setup presented on this paper is based on the
post-distortion technique. It uses a simple circuit
configuration and is a well known technique in the amplifier
linearization, despite being scarcely used in this context.
When applied to mixers, this technique leads to some
advantages especially in the down-conversion process where
the post distorter operates at low frequency and does not need
any extra mixer.
II. POST-DISTORTION
The post-distortion technique is very similar to the
predistortion. The idea beyond this method is to cascade two
nonlinear blocks so that the IMD generated within the two
sub-systems cancels mutually. In this approach the main
block is the first followed by canceling block [5].
Fig 4- Cascade of two nonlinear blocks.
The block diagram above presents a cascade of two
nonlinear circuits. In order to evaluate the nonlinear
distortion effects due to the iteration of the two blocks,
consider the narrowband input signal:
X (ω ) = S (ω )
(1)
Where S( ) is the frequency domain representation of the
input signal, the output of block A will be:
Y1 (ω ) = G A S (ω ) + D A (ω )
Fig 3- Diagram of the frequency retranslation lineariser.
This setup involves two mixing devices. One for the downconversion of the RF signal, while the other is involved in the
up-conversion of the IF distorted signal back into the RF. The
main branch is composed by upper mixer working in a
saturated mode. Then, the IF signal has a strong IMD
distortion component. This signal is sampled at the output
and up-converted and subtracted from a sample of the input
signal in a way that only the IMD components are preserved.
This is the error signal and, after a proper shaping, it is added
to the input signal. The resultant IF signal has a better IMD
performance.
Despite its complexity, this setup has the best IMD
cancellation performance reported. The cancellation level is
about 25 dB, for a phase and amplitude match of 0.1º and
0.1dB respectively.
Nevertheless all these techniques are based on the use of
more than one auxiliary extra mixer or are implemented in the
RF part, which imposes additional design complexity.
(2)
DA(ω) – Distortion generated by the block A.
GA – Gain of block A.
This signal reaches the input of block B where he generates
a signal such as:
Y2 (ω ) = (GAGB )S (ω ) + GB DA (ω ) + DB (ω )
(3)
Where DB( )– Distortion generated by the block B and
GB – Gain of block B.
The total distortion at the output is given by:
Y2 D (ω ) = G B D A (ω ) + D B (ω )
(4)
To cancel the distortion at the output it is required that:
GB DA (ω ) = − DB (ω )
(5)
In order, to eliminate the distortion at the output, the second
block has to generate distortion with the same amplitude of
that generated by the block A when passed through block B,
but in opposite phase.
One possible proposal to the post distorter is presented in
the Fig 5.
Fig 5- Diagram of the post distortion proposal.
This setup presents two branches. From (5) it is clear that it
is necessary to control two independent variables in order to
achieve a proper cancellation. Those variables are the phase
and the gain of the IMD. The upper branch allows to control
the gain of the signal, while the lower branch is responsible
for the generation and phase change of distortion.
series with the flow path of the signal. But, this configuration
imposes a large attenuation to the fundamental tones. The
solution performed comprised an alternate path for the
fundamental tones.
Considering the above, the post distorter is composed by two
branches. The upper one is composed by a gain path (0 dB) to
reduce the attenuation caused by second block. The lower
branch is composed by a series diode. An inductive reactance
is used in order to vary the lower branch output signal phase.
A proper bias of the Schottky diode allows for the generation
of the lower branch IMD power. A resistor is inserted in
series to this path in order to vary the amplitude of the lower
branch signal, allowing a fine tuning of the amplitude.
IV. SIMULATION VALIDATION
First the mixer was characterized by simulations, Fig. 7. The
values of the magnitude and phase of the mixer IMD are
obtained in order to design the proper post distorter.
-20
III. THEORY AND CIRCUIT DESIGN
Output Power [dBm]
-40
The proposed circuit is composed by two main blocks. The
first block is the mixer device and generates undesired IMD
distortion. The second one is the post-distorter and is required
to generate IMD in opposite phase of that generated by the
mixer. The nonlinear element of the post-distorter is a
schottky diode. Assume the mixer is working in a zone where
the phase of the IMD is in opposite phase with the
fundamental tones, which is the usual case. So, the IMD
generated by the diode has to be in phase in relation to the
fundamental tones in order to achieve a good cancellation
performance. Also, the power of the IMD generated by the
diode must be the same of that generated by the mixer to
allow a good cancellation performance. In order to get a fair
IMD generation and the proper phase the diode has to be in
-60
-80
-100
-120
-140
99
99.6
99.8 100 100.2 100.4 100.6
101
Frequency [MHz]
Fig 6- Mixer output.
λ/4
1:n
ZSRF(ω)
vRF(t)
λ/4
ZSLO(ω)
RF
TLIN
IF
LO
ZLIF(ω)
vLO(t)
1:n
λ/4
Idiode
Fig 7- Full circuit showing the mixer and the post distorter.
-20
V. CONCLUSIONS
Output Power [dBm]
-40
A new configuration for mixer linearization is proposed and
validated by simulation. The simulation results are good and
state this technique as an alternative to solve the mixer’s
linearity issue. The post-distortion circuit presented is better
than the previously linearization proposed techniques due to
the very simple circuit designed at low frequencies, which
allows its integration very efficiently.
-60
-80
-100
-120
-140
99
99.6
99.8 100 100.2 100.4 100.6
101
ACKNOWLEDGMENTS
Frequency [MHz]
Fig 8- Complete system output after cancellation.
The authors would like to acknowledge the financial
support provided by Portuguese Science Bureau, F.C.T.,
under Project POCTI/ESE/37531/2002 – OPAMS.
0
Output Power [dBm]
Pout
REFERENCES
- 50
MixerIMD
-100
-150
-30
Linearized MixerIMD
-25
-20
-15
-10
-5
0
Input Power [dBm]
Fig 9- Sweep over RF input power from -30 dBm to 0 dBm
of the mixer and the normalized complete system.
For an input power of -20dBm the resulting mixer IMD
optimization, is presented on Fig. 8. There a 29dB
cancellation was obtained. Figure 9 presents the IMD values
for input power sweep, before and after IMD cancellation. In
that graph the final system was normalized to the output of
the single mixer by adding an extra 5.9dB to the fundamental
and 3*5.9dB to the IMD power. From there we can see that a
minimum of 8 dB cancellation was obtained in all the swept
power, near the compression point. All the simulations were
performed with Microwave Office [7] form Applied Wave
Research using the Harmonic Balance engine.
[1] T. Nesimogulo, M.A. Beach, P.A. Warr and J.R.
MacLeod: “Linearized mixer using frequency
retranslation”. Electronic Letters, 2001, Vol.37,
Nº25.
[2] M. Chongcheawchamnan and I.D. Robertson:
“Linearised microwave mixer using simplified
feedforward technique”. Electronic Letters, 1999,
Vol.35, Nº9.
[3] Ellis T.J., and Rebeiz. G.M.: “ A modified feedforward technique for mixer linearisation”. IEEE
Microwave Symp Dig., MTT-S, 1998, pp. 1-4.
[4] Youngwook Kim, Youngsik Kim, :”Linearized
Mixer Using Predistortion Technique”. IEEE
Microwave and Wireless Components Letters,
Vol.12, NO. 6 June 2002.
[5] Kennington, Peter B. ”High-Linearity RF Amplifier
Design” Norwood MA: Artech House, 2000.
[6] Maas, S. A., Nonlinear Microwave Circuits,
Norwood, MA: Artech House, 1988
[7] “Microwave Office 2002”; Applied Wave Research,
Inc.