Delta-SigmaBased Transmitters Mohammad Mojtaba Ebrahimi, Mohamed Helaoui, and Fadhel M. Ghannouchi
P
ower efficiency is one of the most important parameters in designing communication systems, especially batteryoperated mobile terminals. In a typical transceiver, most of the power is dissipated in the power amplifier (PA) and consequently, it is very important to obtain the maximum efficiency from the PA. A PA operating in Class AB or B is at its maximum efficiency when it is driven by its maximum allowable input power [1]. In practice, the input signal of the PA usually has a varying envelope, and to avoid distortion the PA should not be driven to more than its maximum input saturating power. Unfortunately, this peak power of the input signal happens at very short periods, and most of the time the signal power is around its average power, which is much smaller than its peak power, meaning that, often, the PA works at much lower efficiencies than its maximum efficiency. The power difference is defined as the peak to average power ratio (PAPR) of the signal. For example, for a signal with 12 dB PAPR, a Class B PA would be driven with 12 dB power back-off from its peak input power, and at this power back-off, the efficiency of the PA will degrade from 78.5% to around 20% [1]. Unfortunately, by moving to high throughput modulation schemes, for example, quadrature amplitude modulations (QAMs) such as 16-QAM and 64-QAM mean that more envelope variation is needed to encode the information, and, consequently, lower efficiency is achieved. One well-established solution to this problem is to shape the signal in such a way that all the information lies in the phase of the signal
Mohammad Mojtaba Ebrahimi (
[email protected]), Mohamed Helaoui (
[email protected]), and Fadhel M. Ghannouchi (
[email protected]) are with the iRadio Lab, Department of Electrical and Computer Engineering, University of Calgary, Calgary, Canada T2N1N4. Digital Object Identifier 10.1109/MMM.2012.2226541 Date of publication: 23 January 2013
68
1527-3342/13/$31.00©2013IEEE
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©Digital Stock
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while maintaining a constant envelope for the signal. The PA can then work at its maximum efficiency without any power backoff. In this case, it is possible to use a highly efficient switching-mode PA (SMPA), where maximum efficiency can be achieved without signal distortion [2]–[4]. There are different techniques that can shape the signal to maintain a constant envelope so that the modulated amplitude of the signal can be reconstructed without losing any information [5]–[7]. One of these methods is delta-sigma modulation. By oversampling the signal and using a 1 bit quantizer, the baseband time-varying envelope signal is encoded to a bilevel constant envelope signal. The generated quantization noise at the output of the delta-sigma modulator (DSM) is shaped so that it falls outside of the signal band to maintain a good signal quality. The method is categorized as pulse density modulation, where the information is encoded in the density of pulses [8]–[12]. Figure 1 shows the input and output of a DSM in both time and frequency domains [10]. Figure 2 shows a simple block diagram of a deltasigma-based transmitter. It includes a DSM, frequency up-converter, and a PA, where the PA is fed with a constant-envelope signal to work at its maximum efficiency. While a delta-sigma-based transmitter offers, in principle, some advantages such as linearity and PA efficiency [12], it suffers from two main drawbacks. One of these drawbacks is the need for a high clock speed to oversample the data to achieve good signal quality [10]. To overcome this limitation, parallel processing is often adopted, where parallel DSM branches work simultaneously at a lower speed to provide the same performance as the original DSM [10]. Another problem is the quantization noise, which forms the most part of the signal at the output of the DSM. This quantization noise will be amplified alongside the desired signal by the PA and should be filtered before transmitting, resulting in a very poor overall efficiency for the transmitter [13]. The quantization noise also affects the signal quality. Despite the fact that quantization noise is shaped by the DSM to be out of the signal band, as shown in Figure 1, still some part of the quantization noise is placed in the signal band and degrades the signal quality. Two different figures of merit are used to study the effect of the quantization noise on transmitter performance: the signal-to-noise and distortion ratio (SNDR), and coding efficiency (Ceff) or the ratio of the desired signal to the total power, which is the summation of the quantization noise and desired signal. The first parameter is used to study the performance of the delta-sigma-based transmitter and its corresponding DSM for the in-band noise and the signal quality, and the latter parameter is used to study the effect of the DSM q uantization
69
Signal Power . Total Power (Signal Power + Quantization (2) Noise Power)
Time Domain Representation +1 -1 x(n)
DSM
y(n)
X(f)
Y(f )
Oversampling Ratio = fs/BW Quantization Noise
In-Band Quantization Noise BW/2 Frequency Domain Representation fs/2 f
f
Figure 1. Time domain and frequency domain representations of a delta-sigma modulated signal.
+1 -1
PA
BPF
DSM fc 0
f 0
fs 2
f
fc
f fc
f
f fc
Figure 2. A simple block diagram of a delta-sigma-based transmitter with time and frequency representations of a signal.
Total Power Signal Power SNDR
In-Band Quantization Noise
f Ceff =
Signal Power Total Power
Figure 3. The SNDR and the Ceff definition in DSM.
noise on the transmitter efficiency. The SNDR and the Ceff definitions are as follows [10], [13]: SNDR = 10 log #c
70
Signal Power , m In - Band Noise and Distortion Power (1)
C eff =
Figure 3 also illustrates the concepts of the SNDR and the Ceff. Three types of DSM—low-pass, band-pass and highpass—can be used in transmitter applications. The most popular type of DSM used in transmitters is low-pass DSM (LPDSM) [8]–[10], [14], [15]. Different aspects of the low-pass delta-sigma-based transmitters have been addressed in the literature. An in-band quantization noise cancellation technique was proposed in [8] (see “DSM and Theoretical Analysis of In-Bound Quantization Noise”). At first, the input signal was subtracted from the quantized signal to extract the quantization noise. Then, this quantization noise was filtered by a filter with bandwidth equal to the input signal bandwidth, to separate the in-band quantization noise. At the final step, the extracted in-band quantization noise was subtracted from the quantized signal to improve the SNDR or signal quality of the DSM. In [9], an all-digital architecture for delta-sigma-based transmitters was proposed, where a digital 4 # 1 multiplexer with clock speed equal to four times of carrier frequency was used to upconvert the signal. Parallel processing was used in [10] to decrease the DSM clock speed or increase the signal bandwidth, while maintaining the signal quality. A DSM with eight parallel branches working simultaneously was implemented in this article to increase the bandwidth by eight times. Field-programmable gate array (FPGA) and application-specific IC (ASIC) implementation of a deltasigma-based transmitter using an LPDSM and an SMPA was presented in [14]. In [15], the envelope of a signal was extracted and modulated by an LPDSM and then applied to the power supply of the PA to perform like an envelope tracking transmitter. In the transmitter chain, the LPDSM would be followed by an up-converter to perform like a directconversion transmitter [16], [17]. Consequently, the low-pass delta-sigma-based transmitter inherits most of the advantages and disadvantages of the direct-conversion architecture. A simple front-end with only a single IQ modulator and a local oscillator (LO), without requiring any band-pass filtering at the output of the IQ modulator for suppressing image noise and IF products are just some of these advantages [17]. However, the direct-conversion architecture is very vulnerable to IQ imbalance and has low-frequency noise and distortion problems, including flicker noise, LO leakage, and dc offset, that may degrade the overall linearity of the transmitter [17], [18]. The solution offered to avoid these low frequency effects is to use a band-pass DSM (BPDSM) or a highpass DSM (HPDSM) in the transmitter chain. In these modulators, the signal is located in the IF, usually a quarter (for BPDSM case) or a half (for HPDSM case) of
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the sampling frequency [19], [20]. Consequently, the lowfrequency noise and distortion are avoided. In the case of using BPDSM or HPDSM for transmission, there are two options for driving the PA with the quantized signal. In one solution, the output of the DSM is directly connected to the PA [12], [20]. Here, the clock speed of the BPDSM should be quadruple of the carrier frequency and the clock speed of the HPDSM should be twice the carrier frequency, respectively [12], [20]. For example, for a carrier frequency of 2 GHz, the clock speed of the BPDSM should be 8 GHz, which is not practical. Another solution is to use an IQ modulator or a digital multiplexer as a frequency up-converter [21]. In that case, the clock of the DSM will be independent of the carrier frequency and the transmitter architecture will be a low-IF architecture. As a result, it will inherit low-IF transmitter architecture advantages and disadvantages. The low-IF architecture does not have the low- frequency noise problem and shows better performance in coping with IQ imbalance [17]. However, the structure is more complex and costly
and is not as good as direct-conversion architecture for integration [17]. In [11]–[12], [19], and [21]–[23], the application of the BPDSM-based transmitter was presented. In [11], the application of a BPDSM, followed by an SMPA, was introduced for the first time. In [12], the power efficiency of a RF Class-D amplifier with a BPDSM was analyzed. The coding efficiency of a DSM was introduced in this paper to study the effect of the quantization noise on the transmitter efficiency for the first time, using a WCDMA signal with 10 dB PAPR. In [19], the effect of the BPDSM frequency on the coding efficiency was explained. It was proved in that, while most of the designers choose one-quarter of the sampling frequency as the BPDSM frequency, by choosing 3/10 of the sampling frequency as the modulator center frequency, the coding efficiency of the modulator could be improved by 15%. In [21], an all-digital transmitter using BPDSM was proposed. Similar to [9], for up-converting the signal to the carrier frequency, several digital multiplexers
DSM and Theoretical Analysis of In-Band Quantization Noise In this sidebar, the theory of DSM is explained and then the in-band quantization noise of different DSM, as one of the determinative parameters in selecting suitable DSM topology for transmitter applications, is demonstrated theoretically. It is concluded that the LPDSM and the HPDSM show better signal quality or SNDR than their BPDSM counterpart. Low-Pass, Band-Pass, and High-Pass DSMs Figure S1 shows the block diagram of a first-order DSM. The DSM is based on signal oversampling, quantization, and a feedback loop for quantization noise shaping [31], [32]. The quantizer transforms the amplitude modulated signal to a pulse-shaped bilevel signal and, at the same time, adds considerable quantization noise to the signal. The oversampling operation distributes this quantization noise over a wider frequency band than the signal bandwidth and, therefore, decreases the amount of noise in the signal band. The feedback loop shapes the noise outside the signal band, which further decreases the in-band quantization noise. The noise-shaping effect was previously illustrated in Figure 1. By modeling the quantizer with an adder that introduces a quantization error, e(n), to the signal, in Figure S1, the relation between the output, y(n); the input, x(n); and the quantization error, e(n) in the z-domain representation, can be given by the following equation [31]:
Y (z) = z -1 X (z) + (1- z -1) E (z) . (S1)
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While the input signal appears at the output with just one delay, the quantization noise is multiplied by (1- z -1) . The transfer functions of the output signal to the input signal z -1 and the noise (1- z -1) are called the signal transfer function (STF) and the noise transfer function (NTF), respectively. The NTF in (S1) corresponds to a high-pass filter which suppresses the noise at low frequencies where the input signal is located and improves the system’s in-band SNDR [31]. To achieve better signal quality, higher order DSMs (higher order NTF) can be used at the expense of implementation complexity and risk of instability in DSM [31]. In practice, second- and third-order modulators are usually used, because they offer a good trade-off between signal quality and stability [31]. Besides LPDSM, two other delta-sigma topologies, BPDSM and HPDSM are used for delta-sigma-based transmitters. Unlike the LPDSM, the signal at the input of the BPDSM and the HPDSM should not be a baseband signal, but rather a signal at the IF, where low frequency noise does not degrade the signal quality. The transfer function of the BPDSMs and the HPDSMs
e(n) x(n)
+ -
z-1 1-z-1
y(n)
Figure S1. First-order LPDSM block diagram.
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can be obtained from the corresponding LPDSM by applying the respective mapping functions as follows, where (S2) is used to extract BPDSM from LPDSM and (S3) is used to extract HPDSM from LPDSM [33]:
z -1
LP to BP
- z -2 (S2)
z -1
LP to HP
- z -1 $ (S3)
For example, in Figure S2, a second order LPDSM and its corresponding BPDSM and HPDSM is shown. The BPDSM and the HPDSM are easily have found by replacing z -1 with -z -2 and -z -1 in Figure S2(a). In-Band Quantization Noise of Different DSM Topologies In-band quantization noise is one of the key parameters in designing delta-sigma-based transmitters. Here, we show that the HPDSM exhibits the same amount of in-band quantization noise as its LPDSM counterpart, and both are better than the equivalent BPDSM. Furthermore, we prove that the difference between the SNDR of the LPDSM or HPDSM and the BPDSM can be further increased by adding to the order of DSMs. The in-band quantization noise of BPDSMs is usually avoided or ignored in the literature, although it has a big role on performance of delta-sigma-based transmitters. Equations (S4)– (S6) show the NTFs of an Nth-order LPDSM and its respective BP and HP counterparts:
NTF LP = (1- z -1) N (S4)
NTF BP = (1+ z -2) N (S5)
NTF HP = (1+ z -1) N $ (S6)
By replacing z -1 with e -j2rf fs , the frequency responses of NTFs become:
NTF LP 2 = 2 sin (rf fs) 2
2N
NTF BP = 2 cos (2rf fs) 2
NTF HP = 2 cos (rf fs)
(S7) 2N
, (S9)
2
e 2rms = D (S10) 12
2 s e (f) = D $ (S11) 6fs
The in-band quantization noise power at the modulator output can be calculated as the product
Pq =
#
NTF
2
S e (f ) df $ (S12)
BW
If the oversampling rate (OSR) of the modulator is high enough, usually more than 10 for the in-band frequency components, f fs will be very small. For example, for an oversampling ratio equal to 10, the relative error between rf fs and sin (rf fs) is less than 1.7%. Consequently, functions (S7)–(S9) can be approximated by their first-order Taylor series representations around their center frequencies as follows:
NTF LP 2 = (2 (rf fs)) 2N (S13)
NTF BP 2 = (2 (2rf fs)) 2N (S14)
NTF HP 2 = (2 (rf fs)) 2N $ (S15)
Therefore, the results of (S12) for the respective LPDSMs, BPDSMs and HPDSMs can be calculated as follows:
r 2N 1 e 2 (S16) 2N + 1 OSR 2N +1 rms
Pq -LP =
Pq -BP = 2 2N
Pq -HP =
r 2N 1 e2 2N + 1 OSR 2N +1 rms (S17)
r 2N 1 e 2 . (S18) 2N + 1 OSR 2N +1 rms
Equations (S16)–(S18) show that for the Nth-order DSM, the BPDSM has 22N times more in-band noise power than the corresponding LPDSM and HPDSM. For example, a second order LPDSM theoretically shows a 22*2 times or about 12 dB better SNDR than its BPDSM counterpart; to achieve the same performance in BPDSM, the oversampling ratio needs to be increased 1.74 times.
(S8)
2N
where fs is the sampling frequency. For a randomly-varying signal, if D is the step size of the quantizer, one may approximate the quantization noise by the white noise of a mean square value and power spectrum density (PSD) [31]:
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of the NTF power transfer function and the PSD integrated over the bandwidth:
x(n) + -
1 1-z-1
+ -
z-1 1-z-1
y(n)
-z-2 1+z-2
y(n)
-z-1 1+z-1
y(n)
(a) x(n) + -
1 1+z-2
+ (b)
x(n) + -
1 1+z-1
+ (c)
Figure S2. Second-order (a) LPDSM, (b) BPDSM, and (c) HPDSM.
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were used. In [22], the coding efficiency of a BPDSM, one of the key parameters in designing a delta-sigmabased transmitter, was studied further. While the output of the BPDSM usually feeds the PA directly, there is an option to use an up-converter between the BPDSM and the PA to move the signal from IF to RF to support higher carrier frequencies [22]. The impact of using this up-converter on transmitter efficiency and performance was also studied in [22]. In [23], both two-level and three-level BPDSMs were used and compared for transmitter applications. Using an IS-95 signal at 800 MHz, it was demonstrated that the three-level BPDSM shows a slightly better efficiency performance than its two-level counterpart and improves the efficiency from 31% to 33%. Another option for avoiding the low-frequency noise in delta-sigma-based transmitters is using HPDSM instead of LPDSM. While some papers have mentioned various applications of HPDSM, only in [20] was its application with an SMPA explained. In that case, a single carrier frequency signal was used for testing and an efficiency of 70% was reported, however, without considering the coding efficiency and quantization noise impact on the overall transmitter efficiency. The HPDSM, like the BPDSM, avoids problems of low-frequency noise, dc offset, thermal drift, and 1/f noise. Usually, two signal multipliers (used as a as switching mixer) are placed at the front-end and at the back-end of the transmitter chain, before and after HPDSM. The first multiplier is used to up-convert the signal from the baseband to half of the sampling frequency to use it in HPDSM, and then the second multiplier is used to down-convert the output of the HPDSM to the baseband [24], [25]. In this case, the low-frequency noise in LPDSMs is avoided, while the architecture benefits from the DSM advantages. However, the switching multipliers also inject switching noise into the system. This noise and its effects on HPDSM performance were studied in [26]. The clock speed of HPDSM design was also addressed in [27]–[30], where the time-interleaved parallel processing technique was used to ease the modulator clock constraint. In the time-interleaving technique, multiple interconnected modulators work in parallel and, accordingly, the processing speed of the modulator can be reduced by the number of parallel modulators. While various applications of the three mentioned DSM architectures have been presented, no comprehensive comparison between them for wireless transmitter applications has been made. Moreover, no complete comparison of the transmitter topologies, suitable for each of the DSM architectures, has been carried-out as a guide in selecting the best DSM-based transmitter configuration for a given application. The work presented in this article addresses these concerns by providing an optimized transmitter topol-
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ogy for each of the three DSM types. A qualitative and quantitative comparison is carried-out to highlight the advantages and drawbacks of each topology in actual implementations and to advise designers on which topology they should choose and what parameters they should trade off. This comparison is based on three guidelines: 1) signal quality or in-band noise and distortion, mainly generated by the DSM and the nonlinearities in the transmitter chain 2) ratio of the signal power to the summation of the signal and the noise power or the coding efficiency of the DSM, used to predict the impact of the DSM on transmitter efficiency 3) transmitter complexity, which is determined by the type of selected DSM and its corresponding transmitter architecture.
DSM-Based Transmitter Architectures The output of the DSMs for the LP, BP and HP configurations are located at frequencies of zero, fs/4 and fs/2, respectively. Considering the modulator output frequency, two different architectures can be used for the DSM transmitter: direct-conversion architecture for LPDSM and low-IF architecture for BPDSM and HPDSM [34]–[36]. In the following section, the pros and cons of these topologies are presented.
LPDSM-Based Direct-Conversion Transmitter Figure 4 shows a block diagram of a direct-conversion transmitter based on an LPDSM. In this structure, the modulated signal is directly up-converted to the carrier frequency. The inputs of the IQ modulator will be either +1 or -1 and its output will be a constant envelope signal with four different phases: r 4, 3r 4, 5r 4, and 7r 4, similar to a QPSK modulator [37]. Figure 5 depicts how the IQ modulator generates the constant envelope signal from the quantized I and Q. The equation of the output signal of the IQ modulator of Figure 5 will be as follows:
S out = I 2 + Q 2 cos c ~ c t + tan -1 c 1 mm Q S out = I 2 + Q 2 = 2, +S out = tan -1 c I m = r , 3r , 5r , 7r . Q 4 4 4 4
(3)
The LPDSM-based transmitter architecture’s main advantage is its simplicity and suitability for integration. However, this architecture does suffer from lowfrequency noise and LO leakage.
BPDSM-Based Low-IF Transmitter Figure 6 shows the proposed architecture for a BPDSM-based low-IF transmitter [35], [36]. It consists of two digital quadrature up-converters, two
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Simulation and Implementation Results To study the discussed modulation techniques, the fs fs 0 modulators of Figure S2 f f fc fc+ s fc- s 2 2 2 2 were implemented in MATLAB. An uplink LTE I LPDSM signal with a bandwidth PA of 1.92 MHz and an OSR of BPF fc 32 was used for simulation. 0° + Baseband Figure 8 depicts the simu90° lated power spectra of the three different modulators. LPDSM Q From the power spectrum results, and the theDigital Domain oretical results from the “DSM-Based Transmitter Architectures” section, it f can be seen that the worst f fs 0 - s signal quality is obtained 2 2 from the BPDSM. The simulation results of the Figure 4. Block diagram of an LPDSM-based transmitter. SNDR and the Ceff are listed in Table 1. For a second-order LPDSM and its BPDSMs, one analog quadrature up-converter (IQ HPDSM counterpart, SNDRs of 52.9 dB were achieved, modulator), a PA and a band-pass filter at the output while, as expected from (S16)–(S18), the BPDSM was of the PA. The digital quadrature up-converters are approximately 12 dB lower SNDR at 40.8 dB. There is used to transfer the input I and Q signals from the another factor that impacts the HPDSM-based transbaseband to the quarter of the sampling frequency mitter and degrades its performance considerably. As to be used by BPDSMs. To maintain constant envedepicted in Figure 9, in the case of HPDSM, the signal is lope in the signal that feeds the PA, any filter such as located at the edges of the spectrum ^-fs 2 and fs 2 h, image rejection filter between DSMs and the PA (usually used in conventional low-IF architectures) that and due to the sample-and-hold (S/H) operation in affects the amplitude of the signal should be avoided the digital-to-analog converter (DAC), the signal and [35], [36]. By using digital and analog quadrature upthe shaped noise are repeated at the harmonics of fs converters, shown in the proposed transmitter archi[Figure 9(a)] [38]. At the same time, the signal suffers tecture of Figure 5, there is no image problem, and from frequency response distortion due to the transfer so the PA can be fed directly by a constant envelope function of the DAC (H(f)), mainly because of the S/H signal, generated at the BPDSMs after frequency upeffect [shown in Figure 9(b)] [38], [39]. Consequently, the conversion [35]. f
f
+1
HPDSM-Based Low-IF Transmitter The same architecture as the BPDSM-based transmitter can be used for the HPDSM-based transmitter, except that the digital quadrature up-converters are reduced to two simple digital mixers with LO frequencies equal to fs 2 , and the analog quadrature up-converter frequency is fc - fs 2 . Figure 7 shows the structure of a HPDSM-based low-IF transmitter. The transmitter topologies of Figures 6 and 7 are immune to low-frequency noise and LO leakage, but they have more complex circuits in the digital domain than the topology used in the LPDSM-based transmitter. Moreover, it is noted from (S2) that the BPDSM-based architecture has twice the order of its corresponding LPDSMs or HPDSMs, which means double the implementation area and power consumption.
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-1 I
DSM fc
90°
DSM
0°
+ -
Q +1 -1
Figure 5. IQ modulator operation in delta-sigma-based transmitters.
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f - s 2
f - s 4
f fs 2 3f f fc- s fc- s 4 2
fs 4
0
I + cos(n~sTs/4) + -
+ cos(n~sTs/4) + +
f fs fc+ 4
fc
BPDSM fc-
sin(n~sTs/4)
Baseband
f fc- s 4
fs 4
PA 0° 90°
+ -
f - s 4
0
BPF
BPDSM
Q Digital Domain f f - s 2
fs 4
fs 2
Figure 6. Block diagram of a BPDSM-based transmitter. signal at the edge of the frequency bands will be significantly distorted, as illustrated in Figure 9(b), resulting in a significant degradation in the SNDR and the Ceff of the HPDSM-based transmitters. The S/H also affects LPDSM and BPDSM signals, but its effect is negligible. For example, if we model the S/H of a DAC with a sin c function [39], shown in (4), the signal amplitude will decrease by 2/r at f equal fs/2. If it is assumed that the sin c function only affects the signal not the quantization noise, and Ceff is roughly considered as the ratio of the signal power to the quantization noise power, the HPDSM’s Ceff will degrade by (2/r) 2 times or approximately 0.4 times
comparator as the quantizer. Two DACs, implemented in the FPGA board, are used to generate the quantized I and Q, and an Agilent Technologies vector signal generator (ESG E4438C) is used as a frequency up-converter or IQ modulator to up-convert the signal to a carrier frequency of 1.96 GHz. The output of the signal generator was captured using Agilent Technologies vector signal analysis software (VSA 89600) and vector signal analyzer (PSA E4440A). Figure 10 shows the block diagram and a picture of the measurement setup. A trigger signal was used for easier time alignment between the input and the captured output signals for the SNDR calculation. Figure 11 shows the measured power spectra of all three different types of DSM-based transmitters for an up-link
H (f) = sinc (rf fs) sin (rf fs) .(4) = rf fs By applying the sinc function in simulation, the Ceff of the HPDSM degrades from 9.3% to 4.6%, and, at the same time, its SNDR will degrade approximately 8 dB from 52.9 dB to 44.9 dB, as is shown in Table 1. The modulators of Figure S2 were implemented in an Altera’s Stratix II FPGA for measurement. A DSM consists of delay, adders and subtractors blocks, and a
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f
f - s 2 I
HPDSM fc-
Baseband
cos(n~sTs/2)
Q
fs 2
0 fs 2
f fc-fs
f fc- s 2 PA
fc BPF
0° + 90° -
HPDSM
Digital Domain
f - s 2
0
fs 2
f
Figure 7. Block diagram of an HPDSM-based transmitter.
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-10
-20
-20
-20
-30
(dBm)
-10
(dBm)
(dBm)
Power Spectrum of HPDSM
Power Spectrum of BPDSM
Power Spectrum of LPDSM -10
-30
-30
-40
-40
-40
-50
-50
-50
-30 -20 -10 0 10 20 Frequency (MHz)
-30 -20 -10 0 10 20 Frequency (MHz)
30
30
-30 -20 -10 0 10 20 Frequency (MHz)
30
Figure 8. Simulation results of different DSM structures for an LTE signal with 1.92 MHz bandwidth and OSR = 32.
H(f )
-
f
0
fs 2
fs 2 (a)
fs
2fs
was the same. Second, the quantization noise of the HPDSM is asymmetrical compared to the LPDSM and the HPDSM quantization noise. Figure 10 shows that the upper-band quantization is lower than the lower-band quantization noise for the HPDSM, where the sin c function has a stronger effect on the signal spectrum. The results of the measurements are listed in Table 1.
LO Leakage Impairment Compensation in an LPDSM-Based Transmitter 0
fs 2
fs 2
f fs
(b)
Figure 9. (a) Repeated signal X(f) (solid) and quantization error NTF(f)X(f) (gray) due to the sample and hold and frequency response of the DAC H(f) and (b) output signal of the DAC for HPDSM-based transmitters. LTE signal with the bandwidth of 1.92 MHz and an OSR of 32. The effect of the DAC frequency response on the HPDSM signal can be easily seen in this figure. First, the signal power spectrum of the HPDSM-based transmitter is lower than the signal power spectrums of its LPDSM and BPDSM counterparts, while the signal power, sent to the DAC of the FPGA evaluation board for all cases,
The measured SNDRs for the three DSM topologies, LPDSM, HPDSM, and BPDSM, are reported in Table 1. SNDRs of around 39 dB were obtained for both LPDSMbased and BPDSM-based transmitters, whereas from the discussion in “DSM and Theoretical Analysis of inBand Quantization Noise” and the simulation results, the LPDSM-based transmitter was expected to provide much better SNDR compared to the BPDSM-based transmitter. The reason for this could be either low-frequency noise or LO leakage in LPDSMs. There are some design techniques to mitigate the low-frequency noise effect in a circuit [40]. By implementing the modulators in the FPGA, all modulator circuits and data are treated in the digital domain, and the LPDSM low-frequency noise problem is avoided completely. The LO leakage has yet to be addressed for the direct-conversion transmitter
Table 1. Sndr and coding efficiency comparison of different dsm types.
Modulator Type Order
Sampling Frequency IF Frequency BW (MHz) (MHz) (MHz)
Simulation SNDR (dB)
Measurement SNDR (dB)
Simulation Ceff (%)
Measurement Ceff (%)
LP
2
1.92
61.44
0
52.86
39.7*** 46.9****
9.35
9.6
BP
4
1.92
61.44
15.36
40.76
39.1
9.38
9.7
HP
2
1.92
61.44
30.72
52.86* 44.87**
37.3
9.35* 4.63**
3.0
* without considering DAC frequency response ** with considering DAC frequency response *** **** without LO leakage compensation with LO leakage compensation
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Spectrum Analyzer ESG 4438C Signal Generator
FPGA Evaluation Board DSM
DAC
DSM
DAC
PSA E4440A
I Q
Trigger
IQ Modulator
RF Signal
Vector Signal Analyzer
I Q
IQ Modulator
Ref Clock
Function Generator
Trigger
FPGA Clock
(a) Trigger
FPGA Board (b)
Figure 10. (a) Block diagram and (b) picture of measurement setup.
Conclusion In this article, three different transmitter topologies of delta-sigma-based transmitters—low-pass, band-pass, and high-pass—were reviewed, studied and compared, and their advantages and disadvantages were highlighted. A 1.92 MHz LTE signal with an OSR equal to 32 was used for simulations and measurements to aid in understanding the differences between the architectures. These topologies were compared in terms of signal quality or SNDR, coding efficiency (Ceff) and transmitter complexity. It was theoretically proven that the LPDSM and the HPDSM architectures should provide better signal quality than their BPDSM counterpart. Moreover, the HPDSM and the BPDSM are more complex in implementation and dissipate more power than the LP topology, but are immune to the low-frequency noise, the dc offset and the LO leakage. The effect of S/H on signal quality and coding efficiency was also studied. It showed a significant impact on the HPDSM performance. The S/H effect can prevent the use of the HPDSM topology in transmitter applications, when the efficiency or the signal quality is the important parameter for the design, especially in battery-powered
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radio systems. From the coding efficiency perspective, all of the studied architectures led to the same results. For the signal quality, the HPDSM and the LPDSM theoretically showed the best SNDR. However, in practice, the S/H effect degraded the coding efficiency and the signal quality significantly for the HPDSM scenario. A compensation technique was proposed to reduce the impact of the LO leakage in the case of LPDSM-based transmitters. By applying the proposed technique, the SNDR of the LPDSM-based transmitter was improved by 7 dB, from 40 dB to 47 dB. It is concluded that the best performance can be obtained using the LPDSM-based transmitter if a careful design is considered and appropriate compensation algorithms are adopted. After applying all
Measured Spectrum of DSM-Based Transmitters -30 LPDSM BPDSM HPDSM -40
(dBm)
topologies. This LO leakage can be compensated in the receiver part to improve the SNDR. After down-converting the signal to the baseband at the receiver side, the LO leakage will be converted to a dc component and will appear as a dc offset. To eliminate this LO leakage, the dc offset is calculated and removed digitally from the signal [41]. After taking away the LO leakage from the signal, the measured SNDR of the LPDSM-based transmitter is improved from 39.68 dB to 46.87 dB, much better than its BPDSM and HPDSM counterparts.
-50
-60
-70
-80 1.95
1.955 1.96 1.965 Frequency (GHz)
1.97
Figure 11. Output spectrum of DSM-based transmitters for an LTE signal with 1.92 MHz bandwidth and OSR = 32.
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the required signal processing on the output signals, the measured SNDRs for the LPDSM, BPDSM and HPDSMbased transmitters with the LTE example were approximately 47 dB, 39 dB, and 37 dB, and the measured coding efficiencies were 9.6%, 9.7%, and 3.0% respectively.
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