臺灣博碩士論文加值系統

在本論文中，我們提出一種得到高效能(high performance)超取樣
(oversampling)調變器(modulator)的方法。 此種方法適用在高解析度的
類比/數位轉換器中。針對跳蛙(leapfrog)和串接(cascade)二種架構，發
展一完整的系統分析去得到影響調變器穩定性和類比/數位轉換器系統效
能的控制係數(control coefficient)。首先，對控制係數加以合併以便
得到最少的控制參數。求出整個調變系統的轉移函數(transfer
function)，然後根據轉移函數中的雜訊轉移函數(noise transfer
function)的分母(會產生極點的多項式)，運用根和多項式係數的關係加
以限制控制係數的範圍。再根據機率和統計的觀念，決定出一個穩定系統
極點小於1時各個控制係數分佈的區域。由此穩定區域中,藉由行為模擬(
behavior simu- lation)找出一群可以讓系統得到不錯效能的控制係數。
最後，這二種架構的效能將和傳統的超取樣類比/數位轉換器作一比較。
行為模擬結果顯示，藉由上述所提出的方法求得的控制係數，不但使整個
系統非常穩定，而且系統效能亦不差。在超取樣率(oversampling ratio)
為128的條件下， Signal to Noise Ratio(SNR)可達120dB，Dynamic
Range(DR) 亦可達 125dB。

In this thesis, a methodology to find the high performance
sigma-delta modulators for ultra high resolution A/D converters
is presented. The systematic analysis to obtain the modulator
control coefficients which influence the modulator stability
and the performance of the ADC system is developed for both
leapfrog and cascade architectures. Primarily, the control
coefficients are merged to fewer control parameters. The
transfer functions of the modulation systems are solved, and
then the relationship between the roots and the coefficients of
the polynomial which is the denominator of the noise transfer
function(NTF) of the transfer function is used to constraint
the range of the control coefficients. According to the concept
of probability and statistics, the range of the control
coefficients is determined while the poles of a stable system
must be smaller than 1. By using behavior simulation, we obtain
a set of coefficients with good performance from the stable
region. Finally, the performance of the architectures is
illustrated and compared with those of the conventional
oversampling architectures. In accordance with the results of
the behavior simulation, the systems are not only stable but
also have good performance. For 128 oversampling ratio , Signal
to Noise Ratio(SNR) and Dynamic Range(DR) are higher than 120dB
and 125dB, respectively.