Aug_EDFA_Digital

edfas.org 9 ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 23 NO . 3 The co-simulation of the ΔΣ-modulator is finally presented in the last section. It is started in Simulink, simulates the analogmodel of themodulator withSpectre and the results are processed within the MATLAB 2017b environment. All steps are examinedwith the example of a second-order ΔΣ-modulator based on a switching capaci- tor (SC) technique and a 1-bit quantization. BEHAVIORAL SYSTEM SIMULATION The behavioral simulation is divided into two separate parts, each using a different toolbox. First, an abstract system is created with the ΔΣ toolbox. [1] The second part is the creation and simulation of a Simulink model with the Simsides toolbox. [2] The block diagram of the used architecture is shown in Fig. 2 and consists of two integra- tors aswell as theweighting factors for the integrators and the feedback paths. [3-5] SYSTEM SIMULATION WITH THE DELTA-SIGMA TOOLBOX As a first step, a noise-transfer-function (NTF) is synthe- sized with the ΔΣ toolbox. Therefore, the parameters for the oversampling rate (OSR = 64), the order of the modu- lator (order = 2) and the number of quantization levels (1 bit) are used. With this NTF and a sinusoidal input signal, the output of the ideal modulator can be simu- lated. The output spectrum of the simulation is shown in Fig. 3 as a blue curve. The frequency is normalized by the sampling frequency f S ; the normalized frequency starts at the frequency resolution of 1/8192=1.22×10⁻ 4 because of 8192 simulation steps. In addition, the expected power spectral density (PSD) of the noise is also shown as a pink curve. [1] The obtained signal-to-noise ratio (SNR) amounts to 70.9 dB at the normalized test frequency of 5×10⁻ 3 . The effective number of bit (ENOB) of 11 bits is calculated by: ENOB = (SNR −1.76dB)/6.02dB (Eq 1) SIMULINK MODEL WITH THE SIMSIDES TOOLBOX As a next step, the NTF is mapped into a state-space representation of the modulator. Thus, the weighting coefficients in Fig. 2 are translated into capacitor ratios. [3] These capacitor ratios define the correct behavior of the integrators. Considering the thermal noise constraint for the first sampling capacitor, the calculations lead to the capacitor inTable 1. Basedon the capacitor ratios, amodel with the Simsides toolbox is created as shown in Fig. 4. This model consists of two integrators and an ideal comparator as a 1-bit quantizer. The input signal is the same as before. This model is closer to the model based on transistors because the first integrator has one input branch and the second integrator has two. Another simi- larity is the simulation in the time domain. To verify this Fig. 3 Output spectrum of the system simulation for the modulator (blue) with the ΔΣ-toolbox and expected power spectral density of the noise (pink). Fig. 2 Block diagram of a second order ΔΣ modulator with two integrators and the corresponding weighting factors. [3] Fig. 4 Model of the ΔΣ modulator with the Simsides toolbox.