Method for Converting a PWM Output to an Analog Output When Using Hall Effect Sensor ICs
Method for Converting a PWM Output to an Analog Output When Using Hall Effect Sensor ICs
具有PWM输出的电流传感器是一种非常有用的设备类型。传统上，该设备可以在数字应用中用于主机微控制器可以确定接通时间与传感器输出信号的关断时间的比率。使用PWM传感器的另一种有用的方法是将PWM输出信号转换为模拟输出信号。本文的目标是简要介绍一种简单的方法来将PWM信号转换为模拟信号，以及一些示例和重要的设计约束。
How PWM Output Sensors Work
Before getting too deeply into designing a filter, the first step is to quickly review what the output signal of a PWM sensor looks like. The PWM waveform is basically a square wave, with a frequency we will define as fPWM , and an amplitude that is 0 V for logic low, and VCCfor logic high. From here forward, we will refer to the amplitude as VPWM . The ratio of the signal high time, t上 , to the period (TPWM= 1 / fPWM) is the duty cycle, D. These relationships are diagrammed in figure 1.
PWM输出霍尔IC的占空比与感测磁场成比例。随着输入场的强度增加，D（图2）。相反，当输入字段减小时，D（图3）也是如此。
Figure 1. Basic PWM Definitions
图2.增加字段的PWM
图3.减少字段的PWM
模拟输出传感器如何工作
Now that we reviewed how a PWM output works for a Hall-effect IC, it is time to briefly discuss how an analog output works for a sensor. The premise is nearly identical as that for the Hall IC with a PWM output. Except, instead of a constant switching of the output to generate a signal, the output asserts an analog voltage that is proportional to the sensed magnetic field. For example, when the PWM duty cycle would increase due to a rising input field, the analog output would simply rise to a higher DC voltage, and vice versa for a decreasing field.
Passive Filters
现在,我们来看看有趣的过程的一部分, where we create an analog DC voltage from the PWM output signal. The simplest method for this is with a passive low pass filter. For the purposes of this guide, and for simplicity, the focus will be on passive, first and second order, low pass filters. Passive filters can be realized very simply with resistors and capacitors. The concepts presented here can be applied to more advanced filters.
For the purposes of this document, we will be focusing on analyzing and designing circuits that use passive low pass filters with attenuation roll-off factors of –20 dB / decade for first order filters and –40 dB / decade for second order filters. In some cases, a first order filter will work fine. However, some applications may require a faster response time. In these cases, a second order filter may be necessary. It is up to the end user to evaluate the tradeoff between cost of the filter and the filter performance. The order of the filter can be increased by simply cascading more and more stages. For each additional order of the filter, the roll-off rate becomes steeper, by an additional –20 dB / decade.
There are a couple of ways to compute the filter response to an input signal: time analysis and frequency analysis. I prefer back-of-an-envelope frequency analysis, and will be focusing on using frequency analysis techniques to design first and second order low pass filters. In general, most folks without an electronics background understand frequency methods better than time domain methods when designing simple filters.
Back of the Envelope Filter Design
While there are many detailed ways to compute filter requirements and filter output ripple voltage, I prefer to keep things simple in such a way that I can draw up and design a simple filter on the back of a small envelope and make calculations with a cheap scientific calculator (or smart phone app). The first term you have to define is how much ripple voltage, VRIPPLE , is acceptable in the analog output. The second necessary term is the PWM frequency, fPWM , of the sensor. Once the acceptable VRIPPLE和F.PWMare defined, the required attenuation can be computed. Because we are working in the frequency domain and using known filters, it is most useful to compute this attenuation factor in dB:
where AdBis attenuation, and must be a negative number! Remember that VPWMis simply the output voltage swing of the PWM sensor.
Once the attenuation factor is known we can apply our knowledge, that the slope of a first order low pass filter is –20 dB / decade and the slope of a second order low pass filter is –40 dB / decade, to determine the required 3-dB frequency (f3DB.)的过滤器:
What this equation is telling us is that the attenuation,AdB , is equal to the slope (dB / decade) of the low pass filter, times how many decades are between the 3-dB frequency (f3DB.) and the PWM frequency (fPWM). Since we already know AdB , we will solve the following equation for what we want to know, f3DB. :
Now we have everything we need to design a passive low pass filter. While this may seem a little complicated, trust me, it is easier than solving second order time domain equations.
Another interesting exercise is to set equation 1 equal to equation 2 and solve for VRIPPLE . This will give us an equation that expresses voltage ripple as a function of f3DB. :
而这个方程more complicated than the previous three equations, it has pretty simple mathematics that allow us to plot ripple voltage versus 3-dB frequency for determining known slope, PWM voltage, and PWM frequency.
Figure 4 plots approximate VRIPPLEversus f3DB.for first and second order filter slopes, given fPWM= 8 kHz and VPWM= 5 V. This chart can be used as a guide for designing a filter. Simply select the required amount of ripple on the vertical axis, and then find where the two lines intersect this horizontal line. These intersections are where the filters will achieve the target requirements.
Figure 4. Ripple Voltage versus 3-dB frequency; use for estimating first and second order filters
It should be noted that these calculations will have some error in them when compared to actual measured ripple voltage. One source of error is due to the fact that the corner frequency of the filter is not a perfect corner. It is in fact rounded. This means that the attenuation of the filter near the corner does not follow our 20 dB/decade approximation perfectly. The story is the same for higher order filters as well.
另一个源通过专注于PWM的基频来计算我们的波纹的幅度。实际上，PWM将具有更高的频率内容，因为它是方波。更具体地说，我们省略了基础的奇怪谐波（3×F.PWM, 5 × fPWM , 7 × fPWM , …). Fortunately for us, the attenuation of those higher frequencies from our filter is even greater than for the fundamental. For the most part, they can be ignored for the first iteration of the filter design. As for our back-of-the-envelope calculation, we get very close to the actual value without unnecessarily complicated computations. Oftentimes the first order filter pole must be adjusted downward a little bit to achieve the target ripple, due to the shallower roll-off of –20 dB / decade. The simulations below will illustrate this point.
Example:
Let us say that we have a sensor with an fPWMof 8 kHz, a VPWMof 5 V, and we are targeting LSB / 2 of ripple for our 10-bit A‑to‑D converter. For this case, LSB / 2 corresponds to about 2.4 mV of voltage ripple. So, the first thing we need to do is calculate the attenuation factor we need. Using equation 1:
Now that we know the attenuation factor, the next step is to compute the bandwidth of the filter we need to design, using equation 3. We will do this twice, once for a first order filter:
和again for a second order filter:
So if we use a first order low pass filter, we would need to design a filter with an f3DB.of 3.84 Hz. This may not be attractive depending on the rest of the system requirements. A second order filter would require an f3DB.of 175 Hz. This may be a more attractive option for some applications that require faster transient response.
Building the Filter
Constructing a basic passive low pass filter is quite simple. A first order filter uses one capacitor and one resistor, and a second order filter uses two resistors and two capacitors. The extra resistor, RL , in the schematics (figures 5 and 6) is there to represent a typical input resistance of the measurement system.
图5. 3.77 Hz的一流低通滤波器
Figure 6. Second-Order Low Pass Filter for 175 Hz
We will build the first order filter first. Building a first order filter is as simple as choosing a starting capacitor value, and then computing the resistor value.
Given:
和
For the first order filter (f3DB.= 3.84 Hz), we can chose a capacitor, CF , value of 10 μF and use equation 6 to compute that the filter resistor, RF , value:
RFshould be rounded up to the closest 1% resistor value of 4.22 kΩ, and the corresponding f3DB.value would be 3.77 Hz.
The implementation for a second order passive low pass filter is simply cascading two first order filters in series. In this example, we will create two first order filters, each with an f3DB.of 175 Hz as calculated above using equation 3. For this example, we chose 1 μF for CF和computed RFto be 909 Ω (standard 1% value) by substituting into equation 6:
Simulated Results
以下几个图示出了本文中设计的两个滤波器的仿真结果。PWM输出配置为fPWM= 8 kHz, D = 50%, and VPWM= 5 V，如图7所示。该图表示未过滤的输入信号。请记住，我们将在此波形上施加更慢的过滤器，因此以下许多图形是不同的时间尺度。
Figure 7. Input PWM signal (fPWM= 8 kHz）
Figure 8 illustrates the output transfer function of the waveforms in figure 4 for both the first order (green trace) and the second order (blue trace) filters. It is obvious to see that the lower frequency f3DB.of the first order filter causes a much slower response. It is also apparent that the series resistance of the filter does impact the voltage of the output signal, as there is indeed a resistor divider that reduces the voltage at the system input (4.22 kΩ for the filter and 50 kΩ for the approximated input resistance of the system). Overall, the response of the curves is what was expected from our calculations.
Figure 8. Output Response of first and second order filters
Figure 9. Detail of output ripple for first order filter simulation, ripple = 3.58 mV
Next we need to have a closer look at the ripple voltage of the settled output waveform. Figure 9 shows the detailed view of the ripple of the first order filter output. It shows that the final ripple value is 3.58 mV for our f3DB.of 3.77 Hz. It is a little bit higher than we were targeting, but as stated before, it was expected that we may be off by a little bit, based on our assumptions. However, our filter is definitely performing in that region and could be slightly adjusted. Increasing RFor CFslightly will reduce the ripple. Increasing RFor CFwill also lower f3DB.。仿真实验将显示移动f3DB.down to about 2.57 Hz by changing RFto 6.19 kΩ will bring the ripple into specification.
图10显示了二阶低通滤波器的输出纹波版本中的缩放。在这里，我们可以看到我们更接近我们的原始设计估算。该过滤器实现了2.86 mV的纹波电压。由于我们拍摄了2.4 mV以来不错。再一次，通过稍微和降低F来改变滤波器可以减少该纹波值3DB.in a similar manner as the first order example.
Figure 10. Detail of output ripple for second order filter simulation, ripple = 2.86 mV
Lab Data
A filter design and simulation exercise would not be complete until the filter has been constructed and tested in the lab. The last two figures (11 and 12) are oscilloscope images of the output ripple for each of the two filters. The filters were constructed with the original design components earlier in a solderless breadboard. The input PWM and the output analog voltage were measured using an oscilloscope. The two figures illustrate that our filters performed very close to the original design targets.
Figure 11. First-order filter output lab results, VRIPPLE= 4.0 mV
Figure 12. Second-order filter output lab results, VRIPPLE= 2.8 mV
Conclusion
本文简要总结了一个简单的方法r converting the output of a PWM sensor to an analog voltage. The methods shown use a fairly straightforward method for designing a filter as well as documenting the caveat for using the simple method. The primary goal of showing how to realize a passive low pass filter was illustrated with a first order filter, and a second order filter. The reader can extend the order of the filter in order to increase the response time of the signal while maintaining acceptable ripple. Note: A third order filter rolls off at –60 dB / decade, but requires 2 more passives.
The worked examples show that unless a very slow response time is acceptable, most typical applications will want to pursue a second order (or higher) low pass filter in order to keep the filter response fast enough, and to maintain the use of small components. Increasing the order of the filter increased the number of passive components required to realize the filter. In this case, we went from two total passives to realize a first order filter, to four total passives to realize the second order filter.
Although every system is different, the methods in this document can be used for many different systems. Some PWM signals have a different fPWM。By using the equations documented above, a filter can be designed around a different system. Slower fPWMwill require lower f3DB.，虽然更快PWMcan get away with higher f3DB. . In closing, with a little bit of creative filter design, an off-the-shelf PWM output sensor can be designed into a system that requires an analog voltage.
Copyright ©2013, Allegro MicroSystems, LLC
The information contained in this document does not constitute any representation, warranty, assurance, guaranty, or inducement by Allegro to the customer with respect to the subject matter of this document. The information being provided does not guarantee that a process based on this information will be reliable, or that Allegro has explored all of the possible failure modes. It is the customer’s responsibility to do sufficient qualification testing of the final product to insure that it is reliable and meets all design requirements.
Ref: 296094-AN