Architecture combines low- and zero-IF receivers
A switch-matrix mixer provides the downconversion function in this novel radio.
Heinz Mathis, Institute for Communication Systems, University of Applied Sciences -- EDN, August 26, 2010
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Low-IF (intermediate frequency)-receiver architectures are increasingly popular for many wireless standards. You can detect the signal at the IF or downconvert it to baseband after the ADC stage. This circuit does the final downconversion using a switch-matrix mixer before the analog-to-digital conversion. You use analog filters following the mixer stage. This approach reduces the dynamic range the following ADC stage requires. By doing simulations and taking measurements on a prototype, you can investigate the effect of nonideal switches in the matrix.
Before delving into the details, you should understand the history of this architecture. The superheterodyne receiver has for decades been the architecture of choice because it provides excellent receiver properties, such as selectivity and sensitivity. The architecture does not easily lend itself to integration, however, because you must implement the image-rejection filters in a discrete circuit.
Direct-conversion, or zero-IF, receivers have recently gained importance (Reference 1). This architecture is appropriate for integration, but it causes other problems. A direct-conversion architecture has dc-offset problems that necessitate a dc-nulling strategy (references 2 and 3). In body-worn radio equipment, the antenna’s impedance matching changes frequently. In this case, it is difficult to build a wellbehaved dc-nulling circuit. Furthermore, modern high-speed modulation schemes must have a continuous baseband spectrum without gaps.
To avoid this problem, you can build low-IF, or quasi-direct-conversion, receivers (Reference 2). The desired signal bandwidth after a low-IF-conversion step is on either the positive- or the negative-frequency side, but it does not include any dc part of the spectrum. You can then ac-couple the subsequent ADC.
The final downconversion to baseband usually takes place in the digital domain. You multiply the complex signal with a rotating phasor. Choosing a low IF that is one-quarter of the sampling frequency eases these operations by reducing the number of multiplications to those for swapping samples and changing their signs every other time.
To illustrate this approach, you denote the incoming signal at low IF as s(t) and mix down the signal with frequency fLO (Equation 1):
You then sample Equation 1 with a sampling frequency fS of 1/TS:
You choose fLO to satisfy Equation 3:
Equation 2 then results in Equation 4:
If you represent signal s(t) in its I/Q (inphase/quadrature) form as a real and an imaginary part, you can rewrite Equation 4 as Equation 5:
This form represents the switching function. The major drawback of this technique is if only real analog filters are applied before the analog-to-digital conversion, the ADCs must have a high dynamic range. Wireless-communication equipment has adjacent-channel rejection on the order of 70 dB. In this case, the adjacent channel is the image frequency corresponding to the negative frequency of the desired signal. The ADC must provide more than 12 bits of dynamic range, including the possible signal dynamics of nonconstant envelope-modulation schemes. These ADCs are expensive, and they consume a lot of power.
A possible approach is to apply polyphase filters, which can separately filter the negative and positive frequencies (Reference 4). This approach increases the circuit’s complexity for a given order of filters because the coefficients of such filters are both real and imaginary.
Downconverting the signal from low IF to zero IF before filtering and analog-to-digital conversion eliminates the need for polyphase filters and still uses an ADC with reduced dynamic range.
Architecture and circuit
You can use switches as mixers in downconversion architectures by assuming that you have both the inverse and the noninverse of the real and imaginary parts of the signal (Reference 5). The switch-matrix mixer comprises eight switches operating in four phases that feed the four signals, I+, I−, Q+, and Q−, to the input of a subsequent filter. You can implement the matrix with transmission-gate FET switches. The equivalent operation of these switches is mixing by one-fourth of the sampling frequency (Equation 6):
You insert the switch matrix into the
receiver chain (Figure 1). The numbers assigned to the switches denote
the phases when they are closed. You
drive the switches with phase-shifted
signals (Figure 2). The switching function,
G(t), applies the mixing process
to signal s(t) (Equation 7):
The switching function, G(t), has some harmonics, requiring you to apply some filtering after the mixing process (see sidebar “Fourier coefficients of a switch-matrix mixer,”). You can combine this filter with the ADC’s antialiasing filter.
A low-IF-receiver architecture has
adjacent channels in the negative-frequency
range of the desired signal (Figure 3). A real antialiasing filter can filter
out only adjacent Channel 2. Adjacent
Channel 1 is the image of the
desired channel and passes through the
antialiasing filter without attenuation.
The antialiasing filter must be good
enough to prevent
aliasing from adjacent
Channel 2. The
ADCs require a dynamic
range greater
than 70 dB.
The addition of
the switch-matrix
mixer moves the desired
signal into the
baseband (Figure 4).
The antialiasing filter
must filter out
not only the adjacent
channels but also the
mixing terms from the harmonics of the switching function.
In this case, however, the antialiasing
filter’s bandwidth is half that
of the previous case. Maintaining the
same filter order results in a sharper
antialiasing filter. The filter suppresses
both adjacent channels, dramatically
reducing the ADC’s required dynamic
range.Other channels outside the adjacent channels may fall into the baseband due to mixing with the harmonics of the switch function. To address this problem, you must apply an image filter in front of the switch-matrix mixer. This filter is more relaxed than the antialiasing filter. Both adjacent channels are filtered, so the antialiasing filter allows the ADC to have a lower number of bits.
Simulation results
You can do a simulation using The
MathWorks
Matlab to illustrate the process of an
ideal low-IF mixer (Figure 5). You can
simulate a 100-kHz RF signal with a
strong interferer at 70 kHz. The spectrum
at this point is symmetric, corresponding
to a real signal. A complex-valued
mixer shifts down the signal to
the low IF, making the spectrum asymmetric.
An interferer signal appears at
the image frequency with respect to
zero. Derotating with the remaining
IF yields a zero-IF baseband signal. You
can filter away the interferer using a
real-valued filter.
You can also simulate an ideal switch-matrix
mixer (Figure 6). The first two
plots are the same as those in Figure 5
because the switch-matrix mixer replaces
only the low-IF derotation process.
The third plot depicts that, even with
perfect switches, some spectral interleaving
occurs. You can separate these interlaced higher-order products using
filtering, as the bottom plot shows. Introducing
a gain error causes even more
spectral interleaving (Figure 7). These
additional subbands are filtered off and
do not cause a problem. However, I/Q
imbalance results in the usual image
problem, quantitatively of the same order
as with any low-IF mixer.
A prototype PCB (printed-circuit
board) of the switch-matrix mixer includes
the clock-phase generators
(Figure 8). Lowpass filters surround
the switch-matrix mixers. You mix a
2.40002-GHz RF signal, which is 20
kHz offset from 2.4 GHz, with a 20-kHz
IF using a Maxim
MAX2701 image-rejection mixer. You
send the I and the Q part of the low-IF signal to the test
board. It downconverts
the signal
to a baseband signal
using a clock
frequency of four
times 14 kHz to get
four phases, resulting
in 56 kHz. After
the first mixing
process, the resulting
frequency spectrum
of this signal
has three peaks
(Figure 9). One peak is the image at
−20 kHz, or 40 dB down. The second
peak is the dc offset. The third peak is
the signal of interest at 20 kHz.
After the second mixing process, the
signal of interest now shifts to 6 kHz
(Figure 10). The previous dc peak shifts
to −14 kHz, and the switch-matrix mixer
generates a new dc-offset peak; 40 dB
also suppresses the image of the switch-matrix
mixer at −6 kHz. Choose the
cutoff frequencies of the lowpass filters
before and after the switches as 30 and
15 kHz, respectively.A switch-matrix mixer reduces the dynamic range needed in a subsequent ADC. Apart from the switches, only an additional low-order filter is necessary to prevent unwanted harmonics from falling into the baseband. You can integrate these functions into a single IC.
| References |
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Author's Biography
Heinz Mathis is a professor of mobile communications
at the University of Applied
Sciences (Rapperswil, Switzerland). He
received master’s and doctorate degrees in
electrical engineering from the Swiss Federal
Institute of Technology (Zurich, Switzerland).
His research interests include signal
processing for wireless-communication
systems and positioning systems.
Fourier coefficients of a switch-matrix mixer
You can represent each of the switches in the switch-matrix mixer in Figure 1 of the main text using a Fourier series (Equation A):
The local oscillator frequency is one-fourth the sampling frequency (Equation B):
You can collect the coefficients cMK in a matrix, with m having values of one to four, so that each column presents the Fourier coefficients of the switch function corresponding to the four phases. You can mix down a signal, s(t), representing the low-IF signal in a receiver chain to a baseband signal and represent the switch functions as having real and imaginary parts (Equation C):
You can then represent this signal in a simplified form (Equation D):
You can then apply to equations B and D some algebraic modifications and simplifications (Equation E):
You can then represent the combined coefficients (Equation F):
You can rewrite the Fourier coefficients of the switching functions (Equation G):
Before evaluating the integral of Equation G, look at the special case when k equals zero. Equation G results in the Fourier transforms being equal to ¼; hence, C0 equals zero. The algebraic modifications you make to solve Equation G exclude the case of k being equal to zero, meaning that you needn’t worry about dividing by zero. You then solve the integral in Equation G and feed the result back into Equation F:
If k is even but not equal to zero, since
then Equation H yields Equation J:
If k is odd, since
Equation H yields Equation L:
CK,even is zero for k equals { … , − 11,−7,−3, 1, 5, 9, 13, … }. For all other odd k, namely k equals { … , −13,−9,−5,−1, 3, 7, 11, 15, … }, you have (Equation M):
This allows you to tabulate the values of cK (Table A).
You can represent each of the switches in the switch-matrix mixer in Figure 1 of the main text using a Fourier series (Equation A):
The local oscillator frequency is one-fourth the sampling frequency (Equation B):
You can collect the coefficients cMK in a matrix, with m having values of one to four, so that each column presents the Fourier coefficients of the switch function corresponding to the four phases. You can mix down a signal, s(t), representing the low-IF signal in a receiver chain to a baseband signal and represent the switch functions as having real and imaginary parts (Equation C):
You can then represent this signal in a simplified form (Equation D):
You can then apply to equations B and D some algebraic modifications and simplifications (Equation E):
You can then represent the combined coefficients (Equation F):
You can rewrite the Fourier coefficients of the switching functions (Equation G):
Before evaluating the integral of Equation G, look at the special case when k equals zero. Equation G results in the Fourier transforms being equal to ¼; hence, C0 equals zero. The algebraic modifications you make to solve Equation G exclude the case of k being equal to zero, meaning that you needn’t worry about dividing by zero. You then solve the integral in Equation G and feed the result back into Equation F:
If k is even but not equal to zero, since
then Equation H yields Equation J:
If k is odd, since
Equation H yields Equation L:
CK,even is zero for k equals { … , − 11,−7,−3, 1, 5, 9, 13, … }. For all other odd k, namely k equals { … , −13,−9,−5,−1, 3, 7, 11, 15, … }, you have (Equation M):
This allows you to tabulate the values of cK (Table A).
Talkback
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Mr. Tayloe was not the first to discover synchronous detection using analog switches. An article published by the now defunct Electronics Magazine in the mid-1970s showed how to use the principle for narrow bandpass filters with Qs in the range of 2000 to 10000 ('Narrowband digital filter achieves high Qs' by Thomas A Visel, University of Illinois at Urbana). Around 1975, I independently designed a 'zero-IF' quadrature detector for monitoring the Omega navigation system, which was nearly identical to Tayloe's description. Several years later I worked on a missile instrumentation project and learned that a previous design used a rather more sophisticated application of the principle for signal averaging. Simply put, the architecture is periodically rediscovered but has been around for decades, and is obvious to those skilled in the art, then and now. It might predate the transistor. Mr. Tayloe is but one in a long line of independent discoverers, but happens to have popularized the idea within the amateur radio community. However, despite assertions to the contrary, the idea is not original with him.
Orin Laney - 2010-21-12 23:49:22 PST -
I believe this is an important technique, but to omit any mention or reference to Dan Tayloe's originating work published from 2001-2006 is misleading at best and perhaps intellectually dishonest.
Walter Strifler - 2010-13-9 08:05:03 PDT -
This is definitely a valid and valuable approach, which has been published previously as the "Tayloe Detector", in various Amateur Radio publications. It does indeed make a great deal of sense to use switches as a downconverter. I would point out an error in figure 1, which is that the block with the phase shift should be + 45 and -45, not the 15 shown. Or perhaps the error was intentional, to thwart copyright infringers.
William Ketel - 2010-31-8 19:09:24 PDT -
Never thought direct or low conversion would work with cell phone frequencies, but this is a world different than the kids crystal radio set from gadget freak. Thanks so much for the article because this is obviously the future of radio.
Allan Johnson - 2010-31-8 12:12:45 PDT
