Figure 4.41 additionally depicts the respective AM-AM and AM-PM plots with-out DPD and with SNDPD. The performance, especially for the AM-PM, indicates the limits of the phase noise of the external LO generator.
Submitted by Stefan Trampitsch
Submitted at Institute of Signal Processing
Supervisor and First Examiner Univ.-Prof. Dr. Mario Huemer
Second Examiner
FH-Prof. Priv.-Doz. DI Dr. techn.
Christian Vogel
Co-Supervisors
Dr. Michael Lunglmayr Dipl.-Ing. Daniel Gruber July 2020
JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, ¨Osterreich www.jku.at
DVR 0093696
Modeling and Digital Predistortion of Capacitive Radio-Frequency
Digital-to-Analog Converters
Doctoral Thesis
to obtain the academic degree of
Doktor der technischen Wissenschaften
in the Doctoral Program
Technische Wissenschaften
0 0.2 0.4 0.6 0.8 1 0
0.1 0.2 0.3 0.4
Normalized Input Magnitude OutputMagnitude(V) No DPD
SNDPD 5/1/4
(a) Submitted by
Stefan Trampitsch
Submitted at Institute of Signal Processing
Supervisor and First Examiner Univ.-Prof. Dr. Mario Huemer
Second Examiner
FH-Prof. Priv.-Doz. DI Dr. techn.
Christian Vogel
Co-Supervisors
Dr. Michael Lunglmayr Dipl.-Ing. Daniel Gruber July 2020
JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, ¨Osterreich www.jku.at
DVR 0093696
Modeling and Digital Predistortion of Capacitive Radio-Frequency
Digital-to-Analog Converters
Doctoral Thesis
to obtain the academic degree of
Doktor der technischen Wissenschaften
in the Doctoral Program
Technische Wissenschaften
0 0.2 0.4 0.6 0.8 1
−40
−20 0 20 40
Normalized Input Magnitude
PhaseShift(deg)
No DPD SNDPD 5/1/4
(b)
Figure 4.41: AM-AM and AM-PM of measured wideband RF-DAC without DPD and with SNDPD with J = 5, L = 1, M = 4. The performance was limited by the mea-surement setup, i. e. the phase-noise of the LO (clock) generator.
The presented measurement results validate that the SNDPD is an eective method to signicantly improve the ACPR and the EVM of capacitive RF-DACs.
Due to the physical inspired modeling approach of the RC-DAC's non-idealities, the proposed SNDPD allows for a feasible implementation on an integrated cir-cuit while even outperforming conventional DPD models such as the (generalized) memory polynomial.
as a special case of the GMP (similar to the EMP) which only uses the relevant basis functions corresponding to nonlinear eects caused by the nonideal supply network. This also yields a more robust behavior of the SNDPD model compared to the GMP even when using higher polynomial orders and a larger set of memory taps.
Measurement results proofed the concept and its performance. Two capacitive RF-DAC implementations were used for validation, where for both systems the SNDPD signicantly decreases the EVM and the spectral regrowth. The EVM could be decreased by almost 6 dB for all signal bandwidths. The ACPR is also decreased by up to 7 dB. For dedicated frequency bins the spectral emission is even reduced by up to 12 dB.
The DPD approach for cancellation of the DC-DC voltage ripples was presented to the circuits and systems community [108]. The supply network predistortion approach for capacitive RF-DACs was led with the US patent oce and granted in 2018 [113]. Additionally, a journal paper of the SNDPD approach has been submitted to the IEEE Transactions on Microwave Theory and Techniques and is currently under review.
121
5 Conclusion
This thesis addressed the modeling and digital predistortion for capacitive RF-DACs. The introduced modeling approach using switched state-space models is an ecient method to simulate internal as well as external non-idealities of the capacitive RF-DAC architecture. The digital predistortion cancels the eects of a varying supply voltage on the RF-DAC's output by using a modied parallel Hammerstein model approach, enabling to reduce the stringent requirements of the supply network or improve the linearity of the RF-DAC.
The presented simulation model utilizes a close-to-circuit relation, allowing to simulate and analyze individual, undesired contributors to the nonlinear behavior of the RF-DAC. First approaches using switched linear state-space models provide a fast way of simulating the RF-DAC by using the desired component values of the design. However, internal non-idealities such as the AM-PM distortion can-not fully be covered. Thus, the switched linear state-space model was extended to the switched nonlinear state-space model, covering the AM-PM distortion in-troduced by voltage-dependent on-resistances of NMOS/PMOS transistors in the driving inverters of the capacitive RF-DAC cells. Furthermore, extensions to the switched state-space approach for capacitive RF-DAC modeling, covering crucial non-idealities such as capacitor mismatch, supply voltage variations, and LO phase noise were discussed. The model achieves a good match compared to SpectreRFR simulations and measurements while reducing the simulation run-time by a factor of more than 100.
The proposed supply network digital predistortion approach employs the knowl-edge of the physical behavior of the RF-DAC's behavior and its supply network.
The DPD concept recreates the voltage distortions on the capacitive RF-DAC sup-ply and utilizes this information to modulate the input code to compensate the distortions on the output signal of the capacitive RF-DAC. Computational com-plexity is brought down to a feasible level, enabling an ecient implementation.
The concept was validated by measures taken on two capacitive RF-DAC architec-tures. Furthermore, the SNDPD measurements were compared to state-of-the-art DPD approaches such as the generalized memory polynomial and achieves better performance with even a reduced number of coecients. By applying the SNDPD the adjacent channel leakage ratio over the same bandwidth as the transmitted signal is improved by up to 7 dB for signals up to 160 MHz. For close out-of-band frequencies the spectral regrowth is reduced by up to 12 dB. Moreover, also the in-band linearity, i. e. the EVM, could be improved by almost 6 dB.
123
A Derivations of Nonlinear Models and DPD
A.1 Example to dene Volterra Kernel
This section gives an example of how Volterra kernels can be related to a nonlinear system. The system is assumed to be composed of a LTI system, followed by a memoryless nonlinear system, i. e. a Wiener model. The LTI system is dened by its impulse response h(t) and the memoryless nonlinearity by a 2-nd order polynomial. The output of the LTI system is thus given by
y(t) = Z∞
−∞
h(τ)x(t−τ) dτ . (A.1)
The output of the polynomial is dened as
z(t) =a0+a1y(t) +a2y2(t). (A.2) Hence the total system can be described by
z(t) =a0+a1
Z∞
−∞
h(τ)x(t−τ) dτ+a2
Z∞
−∞
h(τ)x(t−τ) dτ
2
=a0+a1
Z∞
−∞
h(τ)x(t−τ) dτ
+a2
Z∞
−∞
h(τ)x(t−τ) dτ
Z∞
−∞
h(τ)x(t−τ) dτ
=a0+ Z∞
−∞
a1h(τ1)x(t−τ1) dτ1
+ Z∞
−∞
Z∞
−∞
a2h(τ1) h(τ2)x(t−τ1) x(t−τ2) dτ1dτ2 (A.3)
125
where the kernels of the Volterra series can be dened as
h0 =a0, (A.4a)
h1(τ1) = a1h(τ1), (A.4b) h2(τ1, τ2) = a2h(τ1)h(τ2). (A.4c) The system is thus fully described by the Volterra kernels.