f p is equal to, and will be replaced with, f gbw /A DC in later calculations.įigure 3 A graph of the magnitude of A = f gbw / ( j Data sheets don’t commonly specify f p, but they do specify f gbw and A DC, where A DC is the open loop DC gain. Refer to Figure 3 for a graph of this expression using typical values. Here, f is the frequency in Hz, f p is a low frequency pole, f gbw is the GBP, and j = √-1. This is a frequency-dependent parameter equal (to a good approximation in most cases) to f gbw / ( j The op amp gain, A, requires some discussion. For those that don’t, there is a measurement technique which allows each to be determined. Some manufacturers’ datasheets separately call out correlated and uncorrelated currents. Unfortunately, this is not possible at and above the resonance frequency of our filter due to impedance variations with frequency. And so, in the range of frequencies below resonance, matched impedances can offer this beneficial effect. If both bases see identical impedances, the correlated currents produce voltages which cancel and do not contribute to the total noise, just as equal DC bias currents seeing equal resistances would yield cancelling results. However, the difference of the voltages due to the correlated portions must be squared before being added to that sum. The voltages resulting from the uncorrelated portions are among the sum’s squares. These two current types must be handled in computationally different fashions. The uncorrelated parts come from the bases of the individual transistors of the pair. The correlated parts come from equal splits of the emitter bias current and, if present, base bias cancellation circuit currents. The two noise currents from the bases of an input differential bipolar transistor pair contain components which are correlated with one another (hence the equation for i corr) and ones which are not (i m and I p). Generally, the individual noise contributions calculated above are uncorrelated with the others, which means that the total output voltage should be equal to the square root of the sum of their squares. These equations can be solved for the portion of each individual noise source that contributes to the total op amp output voltage: The following equations can be written by inspection of the Figure 2 schematic: And we can simply read the op amp noise source values from their data sheets. Here k is Boltzman’s constant and T = 293.15°K. The voltage noise source for an X ohm resistor at 20☌ is equal to √ (4 It’s convenient to think in terms of the signals in the figure as being volts and amperes per square root Hertz rather than of volts and amperes. Going forward, we’ll focus on the broadband, white noise aspects of these sources.įigure 2 A Sallen-Key low pass filter showing all noise sources. Figure 2 provides a schematic showing the various noise sources that must be considered in the Figure 1 design. Application notes are available which provide an excellent overview of noise analysis. The next step is to develop a means for evaluating noise performance. These results are assumed here and incorporated into this article’s spreadsheet. It also showed that the sensitivity of the response magnitude, at resonance F 0, can be expressed exclusively as a function of Q, C1/C2 and Rf/Rg. 【Download】The QA exchange deck in Solido Crosscheck enables an IP qualification handshakeĪ recent article in EDN described how to calculate R1 and R2 given C1, C2, Rf, Rg, Q and F 0. Therefore, there are four remaining degrees of freedom in the selection of passive components.įigure 1 A schematic of a second order Sallen-Key low pass filter. Although it contains six passive components, the transfer function of the section is fully defined by only two parameters: the resonance frequency F 0 Hz, and the quality factor Q. Assume for the moment an op amp of infinite GBP. It is the goal of this article to derive equations for calculating and managing these parameters and implementing that management in a provided spreadsheet.Ĭonsider the second order topology of Figure 1. These sections exhibit noteworthy differences in noise, component tolerance sensitivities, and op amp gain-bandwidth product (GBP) requirements. When asked for components in the highest Q section of a 1dB, 7 th order, 1kHz, DC gain of 3 Chebyshev filter, one tool offers 220pF and 100nF capacitors with a DC gain of 1, and another 10nF and 31.6(!)nF capacitors with a DC gain of 1.316. Perhaps the simplest justification for my belief is to point out the differences in the answers, to the same request, from two of these tools. Do we really need another design tool for Sallen-Key filters?ĭo we really need another design tool for Sallen-Key filters? Aren’t there enough already? Obviously, you and I think that there’s something more to say on this topic, or you wouldn’t be reading this.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |