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This article looks at the impact of input resistance on the accuracy and resolution of stepped attenuators. By Milan Uskokovic F or those of you who may still be unclear about the whole point of making your own stepped attenuators, let me begin by listing some of their most important advantages over logarithmic volume potentiometers: • lower noise level • longer wear and life span • excellent channel matching in dual (stereo) implementation • better approximation of the log function • better quality/price ratio • flexibility to suit individual application requirements Although these are tangible benefits that outweigh the potential drawbacks (such as lower resolution), the performance and reliability of their final products still remain a major source of confusion and frustration for many DIYers. In my experience, the highest potential for things to go very wrong occurs when not giving due consideration to the issue of load resistance. The effect of the (pre-) amplifier's input impedance is all too often overlooked or not managed properly, and this is precisely what introduces errors in the accuracy and resolution of amateur made attenuators. The rest of this article examines this issue in greater detail and shows you through examples how it can be successfully dealt with in practice. The article offers guidelines for proper calculation of attenuation and resistor values for series- and ladder-type attenuators and provides you with an Excel spread sheet program that, unlike other such programs, takes into account the load impedance of the circuit following the attenuator. RESOLUTION AND ACCURACY The realization that stepped attenuators operate as resistor voltage dividers (Fig. 1) is not a new idea. The output voltage (Vout) of the voltage divider, measured at the resistor Ry, is defined as: (1) However, this calculation is valid for idealized cases only, in which the input impedance (Rina) of the circuit following the attenuator is essentially infinite. In practice, this is not the case, and the value of impedance may be equal to or lower than that of the resistor Ry (Fig. 2). FIGURE 1: Unloaded voltage divider. FIGURE 2: Loaded voltage divider. FIGURE 3: Unloaded four-step attenuator. As a result, the output voltage is lower than when there is no load on the attenuator and it can be calculated as: (2) And here we come to an extremely important point, the one I raised earlier: It is absolutely critical that the input impedance (Rina, as defined by the above formula; usually an amplifier) also be figured in to avoid errors in the accuracy of resolution and attenuation calculations. Although there are two elements to input impedance, the real component (Rina) and the capacitive reactive component (Cina), you may safely omit the latter from the calculations because its effect on the attenuator accuracy in the audio bandwidth is negligible. The value of the component Rina is typically in the range of 1 k-ohm to 1M ”. I will use the four-step attenuator in Fig. 3 to illustrate the error that may occur if the effect of the input impedance of the circuit following the attenuator is neglected. The assigned value of the total resistance (Rall) of the attenuator is 10 k-ohm, load impedance Rina is 10 k-ohm, and the steps are 0, -3, -6, and -9dB. When the output of the attenuator is loaded with a resistance of, say, Rina = 10 k-ohm, the voltage on the output drops significantly below the desired value (Fig. 4). The error per step is as much as 2dB in absolute terms (with the attenuation of -8dB for step 3, instead of the de sired -6dB), while the maximum resolution error occurs between steps 1 and 2, and is 1.6dB. It is evident that the attenuator accuracy becomes looser the lower the value of Rina, and that the effect of Rina on attenuator operation can be safely neglected only at values equal to or exceeding 10*Rall. Otherwise, it is of utmost importance that you consider the value of Rina when calculating resistor values (equation 2) in order to come up with the correct value of each individual resistor in the chain (Fig. 5). The world's leading attenuator manufacturers, who are well aware of these considerations, specify Rina values for optimum performance of their products, often even providing spreadsheets for estimating errors should the product be loaded with a resistance value that is out side their specifications. CALCULATION PROCEDURE First, determine the nominal value
-------------------------- FIGURE 4: Accuracy and resolution error. FIGURE 5: Correct resistor values. FIGURE 6: 24-step attenuator spreadsheet. FIGURE 7: 12-step attenuator. FIGURE 8: Ladder attenuator ”2dB ” step. FIGURE 9: Ladder attenuator ”6dB ” step.
--------------------- of the attenuator Rall for a given value of Rina. In my experience, Rall should take on values between 10 k-ohm and 500 k-ohm, with the following condition holding: 5* Rina > Rall. Thus, for the given value of Rina = 10 k-ohm, for instance, Rall looks to be between 10 and 50 k-ohm. You must now define the number of steps (preferably 24, but a cheaper 12 step version would also do nicely) and determine the attenuator resolution. Although the resolution of any step is adjustable to suit personal preferences, 2dB should normally be enough for the positions most frequently in use during operation (i.e., typically the mid-sec tion), whereas the resolution of the low volume steps may be coarser (Fig. 6). Enter the data in column Satt(n) of the spreadsheet to calculate the right resistor values for each individual step of the attenuator (Column Rn). Since resistors come in only standard values, each calculated resistor value will need to be approximated to the nearest value on the E96 list. Column Rin gives the value of the total resistance that the attenuator presents to the signal source at a given attenuation step. When you enter the value of output resistance of the source device in column Source Z_out, column Sin Att calculates the value of additional attenuation generated by the low, yet significant, output resistance of the source. When you use the spreadsheet for attenuators with a smaller number of steps (12, 14, 16, and so on), enter a sufficiently large value (say, 100dB) in column Sattn(dB) fields for the steps that are not being used. It is important to note that you must choose the same value for all unused steps, as in the case of the 12-step attenuator shown in Fig. 7. The results from column Rin reveal that the input resistance value of the attenuator/amplifier can vary greatly, depending on the switch position, and that it falls with decreasing attenuation. Although the literature and Inter net resources available on the subject often characterize series attenuators such as this as presenting constant resistance to the source, it is worth noting that this holds true only if Rina > 10*Ratt. You may use the spreadsheet (which you can download) for ladder-type attenuator calculations. In that case, only the second line is used to calculate resistor values by separately entering appropriate attenuation values for each step. Similarly, you will need to enter a sufficiently large value (100dB) in column Sattn (dB) for the steps 3 through 24 (Figs. 8 and 9). CONCLUSION You must take into account input impedance of the circuit following the attenuator when designing stepped attenuators in order to avoid errors in attenuator accuracy and resolution. Otherwise, these errors may be so signifi cant as to render useless all the work and resources put into the purchase of high-precision resistors for the project. Also, give due consideration to the proper calculation of steps in case of attenuators with fewer steps (for example, 12), because they have a greater likelihood of error than 24-step attenuators, as well as in cases in which the input impedance of the circuit following the attenuator is lower than the total resistance of the attenuator (R_all). The Excel spreadsheet is a simple program intended to assist in the calculation of correct resistor values and attenuations. It is available for down load at www.audioXpress.com, and may be customized to suit personal preferences. --- Xyz Milan Uskokovic has a Master's degree in electrical engineering and 15 years of experience in designing and building professional audio and video production and post-production systems for broadcasting. Currently, he is working as the chief technical officer at Croatia's Radio 101 and is a licensed project engineer for audio studios, post-production, and sound reinforcement systems. [You can find the spreadsheet program for Milan Uskokovic's article on our website -Eds] [The discussion above is adapted from an article, June 2005, outlined in xyz ] Also see: Single-Ended to Differential-Mode Vacuum Tube Projects Made Easy
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