隨手記錄

DAC Static Specification - 筆記整理

以下為整理「The Fundamentals of Mixed Signal Testing」之內容。英文為原文，所以英文程度好的可直接看原文。中文部分為整理、翻譯過後的資料，僅為自己參考用。

DAC Static Specification

數位 類比 轉換器 的 靜態規格

As the name implies, static DAC parameters are tested at a low frequency, generally at DC. This implies setting a digital input code then measuring the output signal value. In our examination, we discuss the static parameters for a DAC with a linear transfer characteristic. 

顧名思義，靜態 DAC 參數通常是在低頻DC下進行測試。 這意味著先設定好「數位輸入碼」然後再來測量輸出信號值。在檢驗中，我們討論的是具有線性傳輸特性的 DAC 靜態參數。

Important DAC static specifications are：重要的DAC靜態規格有：

◇Resolution 解析度

◇Full scale range 全規模範圍；滿程量範圍

◇LSB size

◇Differential nonlinearity (DNL) - 微分非線性

◇Monotonic 單調

◇Integral nonlinearity (INL) -積分非線性

◇Offset and gain errors - 偏移和增益誤差

◇Accuracy - 準確性、精準度

Two other parameters of interest when testing DACs are 

測試 DAC 時，另外兩個讓人感到興趣的參數是

◇Maximum conversion rate - 最大轉化率

◇Settling time - ˈ穩定時間 | 設定時間

◆ Resolution

An indication of the smallest increment of its output range that the DAC can change. When given in bits, the resolution is the power of 2 which is the divisor for the full-scale range to calculate the minimum DAC output change between successive input digital codes. 

Resulotion(解析度)指的就是DAC在其輸出範圍中，可以更改、變動的最小數值，最小增量。若用位元(n)來表示，解析度 = FSR/2^n，其用來計算在連續的數位輸入碼之間，DAC最小的輸出變化

◆ Full-scale range (FSR)

The maximum extremes of the output signal for a DAC. This parameter varies widely depending on the DAC and can be specified as current or voltage which is positive, negative, or both. Common values are ±2mA, -2mA, ±10V, ±5V, +1.024V. Devices whose output does not cross through 0 are called unipolar while those with ± output polarities are bipolar.

FSR = DAC 輸出信號的最大值。

FSR因不同的DAC而會有很大差異，可以指定為電流或電壓，其值可為正、負或兩者兼具。 常用的值為±2mA、-2mA、±10V、±5V、+1.024V。 輸出不通過 0 的元件稱為單極，而具有 ± 輸出極性的器件稱為雙極。

◆ Offset error 偏移誤差

The difference between the ideal and actual DAC value is when the zero or null level digital input code is presented to the device. This parameter can represent an endpoint code and, on bipolar DACs, can represent the mid-scale code, although this is rare.

偏移誤差指的就是當一個DAC元件其數位輸入碼在「0」或「null level」時，其理想和實際 DAC 值之間的差異。

這個參數可以代表一個端點的代碼，在雙極 DAC 可以代表中段代碼，儘管這種情況很少見。

◆Gain error 增益誤差

Gain error is the difference between the measured output when the full-scale input code is presented and the ideal full-scale output. To make the gain error independent of offset error, the zero scale output of the device is considered as the zero or null point. The gain error is the full-scale output measured value, minus the offset error, minus the ideal FSR.

增益誤差指的是輸入滿階時，理想輸出和實際輸出的之間的差異。為了讓增益誤差獨立於偏移誤差的影響。元件zero scale輸出此時被視為零點。增益誤差是在full-scale時的輸出 - 偏移誤差 - FST

◆LSB size

A linear DAC transfer characteristic is shown as a series of points along a 45-degree line. The binary input code is shown on the left of the figure increment by 1 for each successive code, counting form, for example, 0 to 255 for an 8 bit DAC. The output should in turn increment by

一個線性的DAC其傳輸特性圖，其一系列點所顯示出來的狀況是一條沿著 45 度角的線。而「 二進制輸入碼」顯示在圖的左側，每個連續代碼每次增加 1，例如，對於 8 位 DAC，從 0 到 255。而其輸出值則依照下面公式，依序增加

where FSR is the full-scale output range of the DAC. The definition of one least significant bit or LSB is the expected output change due to a change of input code by the minimum amount. An ideal LSB is calculated from the specified FSR whereas when testing, an LSB is an expected average value based on the actual length of the transfer curve. in other words, it depends on each specific device's offset and gain errors.

其中 FSR 是 DAC 的滿量程輸出範圍。 一個最低有效位或 LSB 的定義是由輸入代碼變更最小量而導致的預期輸出變化。 理想的 LSB 是根據指定的 FSR 計算得出的，而在測試時，LSB 是基於傳輸曲線實際長度的預期平均值。 換句話說，它取決於每個特定設備的偏移和增益誤差。

◆Differential nonlinearity (DNL)

The DAC transfer characteristic found most often is a linear DAC, in which the analog output signal has a 1:1 correlation to a binary digital input code. (other transfer characteristics are, for example, logarithmic output and “rotational” output of degrees.) if a line is drawn between the first and last point of a linear DAC transfer graph, any point which deviates from that line is considered a linearity error. Differential nonlinearity is a measure of the “small-signal” linearity error and is defined as the differential nonlinearity in the output voltage at a specific input as compared to the output at the previous input plus 1 device LSB.

最常見的 DAC 傳輸特性是線性 DAC，其中類比輸出信號與二進制數位輸入碼具有 1:1 的相關性。 （其他傳輸特性是，例如，對數輸出和度數的“旋轉”輸出。）如果在線性 DAC 傳輸圖的第一個點和最後一個點之間畫一條線，則偏離該線的任何點都被視為線性誤差。微分非線性是“小信號”線性誤差的量測，定義為特定輸入的輸出電壓與前一輸入的輸出加上 1 個元件 LSB 相比的微分非線性。

◆ Monotonic

A word to state that, with increasing input code, the output stays the same or increases and vice versa. This quality of a DAC is very important if it is used in a feedback loop. When a non-monotonic device is used in a feedback loop, the loop can get “stuck '' such that the DAC toggles (or oscillates) forever between 2 input codes. monotonicity is guaranteed if DNL is less than ±1LSB. It is often specified as a number of bits that is equal to or less than the resolution of the device, e.g. a 14 bit DAC may be specified as “monotonic to 12  bits”.

用一句話來說明：隨著輸入代碼的增加，輸出保持不變或增加，反之亦然。 如果在反饋迴路中使用 DAC，則該 DAC 的品質就非常重要。 當在反饋環路中使用非單調設備時，環路可能會“卡住”，以至於 DAC 在 2 個輸入代碼之間永遠切換（或振盪）。 如果 DNL 小於 ±1LSB，則可保證其單調性。 它通常被說明為等於或小於設備分辨率的位數，例如 14 位 DAC 可以指定為“單調到 12 位”。

◆ Integral nonlinearity (INL)

If differential nonlinearity is small-signal linearity error, integral nonlinearity is the large-signal nonlinearity error. integral nonlinearity is the cumulative effect, for any given input, of all differential nonlinearities. It may also include other sources of nonlinearity, the classic case being that of DAC output voltage changing because of resistive heating effects as DAC currents change in the R/2R ladder. Integral nonlinearity is measured by testing how far a given output deviates from a line drawn between the transfer function endpoints.

如果微分非線性是小信號線性誤差，積分非線性是大信號非線性誤差。 積分非線性是對於任何給定輸入，所有微分非線性的累積效應。 它還可能包括其他非線性源，典型的情況是 DAC 輸出電壓隨著 R/2R 梯形圖中 DAC 電流的變化而發生電阻加熱效應而發生變化。 積分非線性是通過測試給定輸出偏離傳遞函數端點之間繪製的線多遠來測量的。

◆ Accuracy 準確性、精準度

How well a DAC matches a perfect device. This includes the errors noted above and may be given in percent of reading similar to the way voltmeters are specified. It is calculated from static errors, not measured directly.

DAC 與完美設備的匹配程度。 這包括上面提到的誤差，並且可能以類似於電壓表指定方式的讀數百分比給出。 它是根據靜態誤差計算的，而不是直接測量的。

◆ Maximum conversion rate 最大轉換率 

This parameter is somewhat self explanatory. As a DAC’s input changes, its output must be given time to reach the output level and settle. The value of this parameter should include the worst case rate, which is most likely the inverse of the time required to change from zero scale to full scale output.

這個參數有點不言自明。 當 DAC 的輸入端發生變化時，其輸出端則必須花費一點時間，去達到輸出準備並且穩定下來。 此參數的值應包括最壞情況速率，這很可能是從零量程變為滿量程輸出所需時間的倒數。

◆ Settling time 穩定時間 | 設定時間

Essentially the same as op-amp settling time. It is the time required for the output to reach and remain within ±1/2LSB of its final value or within some other defined limit. it may be expressed in LSBs or in %FSR, for example, ±0.1%.

本質上DAC與運算放大器的settling time是相同的。 settlilng time是輸出訊號達到穩定的時間。它是輸出達到並保持在其最終值的 ±½LSB 內或其它定義的限制條件內所需的時間。 可以用LSBs或%FSR來表示。例如±0.1%FRS。

直接翻譯後，效果好像也不太好，不容易理解。可直接參考下面的連結，應該會好懂一些

⬜ ADC特性參數筆記 - Offset Error、Gain Error、INL、DNL