ANALOG DEVICES AN-252 APPLICATION NOTE ONE TECHNOLOGY WAY e P.O. BOX 9106 NORWOOD, MASSACHUSETTS 02062-9106 617/329-4700 Using the 2S80 Series Resolver-to-Digital Converters with Synchros: Solid-State Scott-T Circuit by Mark Schirmer INTRODUCTION The 2580, 2581, and 2S82 are monolithic, tracking con- verters that are designed to interface to four-wire resolver format signals with nominal 2V rms ampli- tudes. These devices can also be used with synchrc format signals if an external circuit is employed whict accomplishes the transformation from synchro tc resolver format. Traditionally, this conversion has been accomplished with a Scott connected transformer, com- monly referred to as the Scott-T transformer (Figure 1). While a well designed Scott-T transformer makes for a very simple galvanically isolated synchro-to-resolver conversion system, the high cost and large size of trans- formers (particularly when operating at 60Hz) may negate the benefits of a monolithic resolver-to-digital converter. OP AMPS ARE AD648, AD712, OR AD713 S1 1:Rn $1 SIN $3 $3 1:Rm $4 cos $2 $2 Figure 1. Synchro-to-Resolver Format Scott Connected Transformer If the design does not require the galvanic isolation intrinsic to the Scott-T transformer, a simple solid-state circuit like that shown in Figure 2 can be used. By using precision resistors and/or trimming the circuit, perfor- mance can be achieved comparable with high quality Scott-T transformers, while realizing considerable sav- ings in cost and size. REF (2V rms) SIN (2V rms) Figure 2. Solid-State Scott-T CircuitRESOLVERS AND SYNCHROS tion signal applied to the primary (rotor) is inductively The resolver is an electromagnetic, rotational device that coupled to the secondary (stator). The transformation detects angular displacement. An equivalent electrical ratios are amplitude modulated by the sin and cosine of representation and diagram of typical output signal for- the angle of the rotor relative to the stator. mats for a resolver are shown in Figure 3. An ac excita- ceosst\ \ A a arnt ANa ANN Sr (COs) yy YVVY ad ATTY R2 $4 $3T0 S1 AMAA A aANN Nita ROTOR STATOR sme VV VVV YVVY VV re ero AN ANANAANAAAAR AANA VV VV VV VV AVY 0 90 180 270 360 Figure 3. Electrical Representation and Typical Resolver Signals The operation of the synchro, Figure 4, is very similar to configuration, spaced 120 degrees apart, while the that of the resolver. The fundamental difference is that resolver has two isolated windings separated by 90 the stator windings of the synchro are connected in a degrees. crow lAN Ara aaAANAAAA aA VU OV S1 $3 RI sstoss LALA, ANNANAaA. dD, AANA vue SRPVVV VV VVV srs eShhhthphnntaAhhhhnan fe VVVVYVVYY TYVVVV VV? 82 arom AAANAAAANAAAANAAAA VVVVVVVVVVVVVVVVVVY o 90 180 270 360 ROTOR STATOR Figure 4. Electrical Representation and Typical Synchro SignalsTHEORY OF OPERATION The solid-state Scott-T circuit illustrated in Figure 2 uses two operational amplifiers to transform a synchro for- mat signal into a resolver format. A third amplifier is used to provide a differential input for the reference signal. The synchro format input voltages can be written in the form: Vs3-s1 = KVaer sin 0 (1) Vso53 = KVper sin (0 +120) (2) Vsi_so = KVper sin (@ +240) (3) where K is the transformation ratio of the transducer and 6 is the shaft angle. In the above notation, Vg, 5, refers to voltage between synchro stator terminals Si and Sj. The order of the indices indicates the polarity/phase of the signal, e.g., Vsa-si represents the voltage at S3 measured with respect to $1. The above assume that the reference volt- age applied across the rotor of the synchro is of the form: Veer = Vai-Va2 = Vo sin wt (4) The normal convention is for R1 to be taken as the high potential side of the reference excitation, thus making the quantity Vg,,2 positive, i.e, for shaft positions between 0 and 180, Vc3_5, will be in time phase with Vai_-r2- These conventions are consistent with those of MIL-S-20708. The objective of the circuit is to convert synchro signals to resolver format signals of the form: Vs5-s1 = KVeee sin 8 (SIN) (5) Vso sq = KVae- cos @ (COS) (6) where for a resolver, the reference voltage is taken as: Veer = Vao-Vag = Vo sin wt (7) Equations 5, 6, and 7 are based on the conventions used in MIL-R-21530 for the case where the reference excita- tion is applied across the R2-R4 rotor winding and R2 is taken as the high potential side. MIL-R-21530 is essentially a specification for a brush type resolver. Brushless resolvers, typically with a single rotor winding, may use a different phasing convention. If it is desired to use this solid-state Scott-T circuit to emu- late a brushiess resolver, the resolver manufacturer's phasing equations should be consulted for consistency with Equations 5, 6, and 7. Different phasing conven- tions will result in positional offsets in multiples of 90 and/or sense of rotation reversals. The signal represented by Equation 5 is directly satisfied by one of the synchro signals, Equation 1. Operational amplifier A2, acting as a differential inverting buffer, inverts Vs,_s3 thus producing the resolver SIN signal. The Zener diodes on the inputs simply limit the applied voltages to the amplifier to guard against component damage. The series input resistors may be scaled to adjust the gain/attenuation of the amplifier. The second resolver signal, Equation 6, can be shown to be a linear combination of the signals in Equations 2 and 3: Vs2-s3 Vsi_s2 = KV sin at (sin [@ + 120] sin [@ + 240]) (8) Using the trigonometric identity: sin (A + B)= sin Acos B + cosA sinB (9) it is then possible to show that sin (0 + 120) sin (6 + 240) = sin 6 cas (120) + cos @ sin (120) sin @ cos (240) cos 6 sin (240) ~ ine 3 oateine 3 = 3 mn + > cos +5510 + 3 cos = V3c0s 0 (10) Operational amplifier A3 is configured as a differential summing amplifier and accomplishes the computation function: Vs3-s2 + Vsi_-s2 = (Vg2-s3-Vs1-52)*-cos@ (11) Since A3 also inverts the input signals, the output of A3 is thus the resolver COS signal. The feedback resistor, R2, and series input resistors, R3, are chosen such that the gain of the amplifier is 1/\/3 for 2 V rms inputs and scaled proportionately for other sig- nal levels, i.e., R22 R383 \V/3Vrms Since it is unlikely that the exact value of this resistor ratio can be obtained, it is suggested to use a slightly higher value for R2 and trim the output to the desired level using the potentiometer as shown in Figure 2. RESISTIVE SCALING FOR HIGH VOLTAGE SYNCHROS Since the 2580, 2881, and 2S82 all require nominal 2 V rms input signal amplitudes, it may be necessary to adjust the signal levels from the synchro. This can be easily accomplished by adjusting the values of the input resistors (R3, R4) to the op amps shown in the sche- matic. Note that because the amplifiers may be operat- ing at less than unity gain, internally compensated amplifiers are recommended in order to reduce the sus- ceptibility to oscillation. The AD712 (dual), AD713 (quad), and AD648 (dual) are suggested. (12) In addition to galvanic isolation, transformer coupling also significantly improves the common mode rejection on the inputs to the converter. The circuit shown in Figure 2 also enhances the common made rejection of the system by virtue of the differential amplifier config- uration of the circuitry on both the reference and signal inputs. As with any differential amplifier, the commonmode rejection ratio will be enhanced with closely matched resistance on the inverting and noninverting inputs of the operational amplifier. For example 0.01% tolerance resistors will yield a typical 80 dB CMRR with a worst case of 68 dB. The table below summarizes suggested values of the resistors in the circuit for various standard synchro volt- ages. The values indicated are standard values for pre- cision (1% or better) resistors. The last entry in the table gives generalized formulae for the resistor values as a function of an arbitrary signal voltage. In addition, please note that the value of R4 may differ in the signal and reference differential amplifier circuits (e.g., an 11.8 V signal synchro is often excited at 26 V rms). Signal Voltage (V rms)} R1 R2 R3 R4 2.0 11K | 12.7K 22.6K | 11.3K 11.8 11K | 12.7K 133K | 66.5K 26 11K | 12.7K 280K | 140K 90 11K | 12.7K 1.18M | 590K 115 (REF only) KI - - 620K Vv R 1.155*R | V*R VFR/2 CIRCUIT ACCURACY The accuracy of the solid-state Scott-T circuit is deter- mined primarily by the accuracy of the resistors. While absolute values are not critical, the resistors should be matched in pairs on the inputs to the operational ampli- fiers in order to obtain maximum accuracy. Typically, 0.1% or better tolerance values are best. Most critical is to maintain the ratios of R1:R2 = 1.1547 and R3:R4 = 2. Note that the number of different resistor values required can be reduced if R4 is constructed by using two resistors of value R3 in parallel (alternatively, R3 can be two R4 value resistors in series). In either case, the use of resistor networks may offer significant cost and size reductions. If 0.1% tolerance resistors are used, the angular errors introduced by the solid-state Scott-T circuit will range from 2 arc minutes (typical) to 7 arc minutes (maxi- mum). This is additional error which must be added to the accuracy specification of the converter in a worst case analysis. Substantially better accuracy is achievable through the use of matched pairs and/or networks, as the angular errors are proportional to resis- tor inaccuracies. If the necessary precision resistors can not be obtained, it is suggested that the gain of the COS circuit in Figure 2 be increased by increasing the value of R2. The output of the circuit may then be attenuated using a potentiometer so that its gain is precisely matched to that of the SIN circuit.