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Required output load ‘VA’ Power Requirements
Regarding your D/S or D/R converter function modules, you specify a ‘VA’ output capability. I assume ‘VA’ stands for Volt Amperes. For a given load (Synchro or Resolver), how do I calculate the required output load ‘VA’ power requirements?
An important consideration in selecting a D/S-R converter is to make sure it has sufficient drive capability for the intended load. Drive capability is specified as VA (Volt Amperes) since actual CT’s or CDX’s (Control Transformers Or Control Differential Transmitters) have an Inductive impedance. The key parameter needed to calculate required VA for the Synchro/CDX or Resolver load device is Zso. For a 3-wire Synchro, or a CDX, Zso is the equivalent impedance with two of the stator inputs tied together and measured to the third stator lead. The Zso for a given CT/RT/CDX is specified by the manufacturer. For resolver RT’s, Zso is the impedance of one of the two input stator windings.
To calculate the VA required for a Synchro CT or CDX load:
VA = ¾(VL-L)² / |Zso|, where VL-L is the D/S Line to Line output voltage and |Zso| is the magnitude of Zso.
An example of a very common military CT is the 11CT4e, Zso = 700 + j4900 Ω and |Zso| = 4,950 Ω.
Therefore, the VA required to drive an 11CT4e Synchro control transformer is: VA = ¾(90)² / 4950 = 0.75(8100) / 4950 = 1.23.
A CDX output is usually connected to a CT. The total load on the D/S would be the sum of the CDX VA requirement and the CT VA requirement, each calculated based on their respective Zso values.
For Resolver RT loads, the calculation of VA is VA = (VL-L)² / |Zso|.
For a typical 11.8 V L-L, size 08, RT, |Zso| = 173 Ω, and VA = (11.8)² / 173 ≈ 0.80.
Compare the result against the per-channel VA rating of the D/S variant you are considering; the ratings by variant are tabulated in the DS MODULE GUIDE. If the required VA is greater than what is available from the selected D/S, you can either use a Synchro or Resolver Boost Amplifier, or reduce the load’s VA demand by “tuning” it with AC capacitors as described in the next question. Nominal Zso values for standard military synchro types are tabulated in the last question on this page.
The load needs more VA than my D/S channel can deliver. Can I tune the load with capacitors instead of adding a boost amplifier?
Yes, in many cases. Most of the VA a control transformer draws is reactive (the j4900 Ω part of the 11CT4e impedance above, versus only 700 Ω of resistance). A set of matched capacitors placed across the synchro lines supplies that reactive current locally, so the converter only has to deliver the resistive part. The method below is adapted from the Synchro/Resolver Handbook, Chapter 4, “Tuning Synchro and Resolver Control Transformer Loads”.
Connection. For a 3-wire synchro, three equal capacitors are connected line-to-line across the stator: S1–S2, S2–S3 and S3–S1 (Handbook Fig. 4-27). For a resolver, one capacitor is placed across each stator winding, S1–S2 and S3–S4 (Handbook Fig. 4-28), and the calculation is the same.
Capacitor value. With Zso = Rso + jXso and reference frequency f:
C = Xso / ( 4πf (Rso² + Xso²) )
Note that the Handbook’s formula uses 4πf, not 2πf; using 2πf would give twice the capacitance.
Worked example, 11CT4e at 400 Hz (Zso = 700 + j4900 Ω):
- Rso² + Xso² = 700² + 4900² = 2.45 × 107 Ω²
- 4πf = 4 × π × 400 ≈ 5.03 × 103
- C = 4900 / (5.03 × 103 × 2.45 × 107) ≈ 3.98 × 10-8 F ≈ 40 nF per capacitor
Power after tuning. The VA drawn once the reactive current is cancelled is:
VAtuned = VAuntuned × Rso / |Zso|
For the 11CT4e: VAtuned = 1.23 × 700 / 4950 ≈ 0.17 VA, down from 1.23 VA untuned. A tuned load can therefore often be driven from a lower-power D/S tier than its untuned VA would call for, provided the channel’s output voltage range still covers the load (a 90 V L-L synchro still needs a 90 V-capable channel).
Precautions (paraphrased from the Handbook):
- The capacitors must be rated for AC operation at the line-to-line voltage; do not use DC-rated parts.
- The three capacitors must be closely matched. Unequal values shift the phase of the lines by different amounts, which creates quadrature signals in the loop. Quadrature is often tolerable, but it can saturate servo error amplifiers, cause asymmetrical limiting, and it makes any phase shift on the reference more critical. See Phase Shift Limits and Quadrature Error.
- If the synchro or resolver is ever disconnected while the capacitors remain wired to the converter output, the capacitors alone present a heavy (purely capacitive) load to the converter.
The full derivation, the figures and the impedance tables for common CT, resolver and torque-receiver loads are in Synchro/Resolver Handbook, Chapter 4 (PDF, naii.com Application Notes → Instruments), pages 32–34. A naii.com login is required to download the PDF.
Where do I find Zso and the other parameters for a standard military synchro?
The manufacturer’s data sheet governs, but for the standard MIL-type synchros the nominal values are well established. The tables below give typical parameters of standard synchros and resolvers (adapted from the Synchro/Resolver Handbook, Appendix A, Figs. A-1 to A-3). They are nominal 1980-era catalogue values; confirm against the data for the actual part before finalizing a design.
Reading the type designation. A designation such as 11CT4e breaks down as: frame size (11 = 1.1 in. diameter), type (CX control transmitter, CT control transformer, CDX control differential transmitter, TX torque transmitter, TR torque receiver), reference frequency code (4 = 400 Hz, 6 = 60 Hz) and a modification letter. A “26V” prefix means the unit belongs to the 26 V reference / 11.8 V L-L system; without the prefix it is a 115 V reference / 90 V L-L device.
Reading the impedance columns. Zro is the rotor impedance with the stator open, Zrs the rotor impedance with the stator shorted, Zso the stator impedance with the rotor open, and Zss the stator impedance with the rotor shorted. Zso is the value used in the VA formulas above. Values are in ohms as R + jX. “Phase lead” is the time-phase lead of the output voltage relative to the excitation; a D/S channel has negligible inherent phase shift, so if a simulated channel must reproduce a specific synchro’s phase lead the DS Set Phase Offset register (±90°) in the DS1-DSN Manual can be used. A dash (—) means the source table left the cell blank.
Synchro Control Transmitters (CX)
| Type | Freq (Hz) | Rated V | No-load input V | No-load input A (max) | No-load input W (max) | Rotor DC R (Ω) | No-load output V | Phase lead (°) | Stator DC R (Ω) | Zro (Ω) | Zrs (Ω) | Zso (Ω) | Zss (Ω) | Stator error (arc-min) | Residual fund. (mV) | Residual total (mV) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26V 08CX4(B1) | 400 | 26 | 26 | 0.111 | 0.95 | 60 | 11.8 | 13.0 | 19 | 77 + j270 | 137 + j39 | 17 + j49 | — | 10 | 20 | 40 |
| 26V 06CX4c | 400 | 26 | 26 | 0.153 | 0.86 | 26 | 11.8 | 8.0 | 10 | 32 + j185 | 70 + j23 | 9 + j32 | 12.5 + j2.7 | 7 | 20 | 30 |
| 26V 11CX4c | 400 | 26 | 26 | 0.130 | 0.56 | 21 | 11.8 | 4.5 | 20.6 | 34 + j265 | 51 + j21 | 7.7 + j45 | 8.7 + j3.2 | 7 | 12 | 19 |
| 11CX4e | 400 | 115 | 115 | 0.031 | 0.61 | 343 | 90 | 4.5 | 300 | 550 + j4070 | 725 + j307 | 330 + j2080 | 387 + j147 | 7 | 45 | 75 |
| 15CX4d | 400 | 115 | 115 | 0.085 | 1.41 | 97 | 90 | 3.6 | 86 | 179 + j1400 | 217 + j125 | 100 + j775 | 112 + j63 | 6 | 32 | 60 |
| 15CX6b | 60 | 115 | 115 | 0.056 | 2.4 | 550 | 90 | 15.0 | 470 | 628 + j2210 | 1170 + j299 | 367 + j1190 | 630 + j143 | 7 | 75 | 110 |
| 18CX4d | 400 | 115 | 115 | 0.110 | 1.32 | 25 | 90 | 1.0 | 37 | 78 + j2210 | 78 + j81 | 52 + j598 | 40 + j39 | 6 | 40 | 60 |
| 18CX6e | 60 | 115 | 115 | 0.040 | 1.11 | 559 | 90 | 10.0 | 666 | 605 + j3130 | 1380 + j451 | 510 + j1580 | 740 + j150 | 8 | 30 | 85 |
| 23CX4d | 400 | 115 | 115 | 0.245 | 2.95 | 15.5 | 90 | 1.8 | 11.8 | 31 + j530 | 31 + j36 | 15 + j263 | 15.7 + j17.7 | 6 | 32 | 48 |
| 23CX6d | 60 | 115 | 115 | 0.080 | 1.74 | 195 | 90 | 6.0 | 276 | 242 + j1650 | 462 + j150 | 211 + j954 | 319 + j62 | 8 | 30 | 60 |
Synchro Control Transformers (CT)
| Type | Freq (Hz) | Rated V | No-load input V | No-load input A (max) | No-load input W (max) | Rotor DC R (Ω) | No-load output V | Phase lead (°) | Voltage gradient (V/°) | Stator DC R (Ω) | Zro (Ω) | Zrs (Ω) | Zso (Ω) | Zss (Ω) | Stator error (arc-min) | Residual fund. (mV) | Residual total (mV) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26V 08CT4(B1) | 400 | 11.8 | 10.2 | 0.137 | 0.47 | 28 | 22.5 | 13.5 | 0.39 | 145 | 173 + j564 | 253 + j104 | 25 + j93 | — | 10 | 30 | 60 |
| 26V 08CT4c | 400 | 11.8 | 10.2 | 0.023 | 0.057 | 99 | 22.5 | 8.5 | 0.39 | 423 | 607 + j2900 | 800 + j300 | 100 + j506 | 140 + j53 | 7 | 25 | 30 |
| 26V 11CT4d | 400 | 11.8 | 10.2 | 0.086 | 0.184 | 16.7 | 22.5 | 6.0 | 0.39 | 87 | 130 + j716 | 151 + j73.5 | 20 + j128 | 27 + j13.8 | 7 | 15 | 18 |
| 11CT4e | 400 | 90 | 78 | 0.018 | 0.31 | 529 | 57.3 | 4.5 | 1.0 | 347 | 510 + j3020 | 535 + j302 | 700 + j4900 | 900 + j515 | 7 | 32 | 60 |
| 15CT4c | 400 | 90 | 78 | 0.010 | 0.165 | 897 | 57.3 | 4.2 | 1.0 | 589 | 837 + j5170 | 943 + j589 | 1020 + j8330 | 1500 + j982 | 6 | 32 | 60 |
| 15CT6d | 60 | 90 | 78 | 0.013 | 0.21 | 1300 | 57.3 | 9.5 | 1.0 | 900 | 970 + j3800 | 1430 + j409 | 1140 + j6240 | 2280 + j836 | 6 | 45 | 65 |
| 18CT4c | 400 | 90 | 78 | 0.007 | 0.07 | 863 | 57.3 | 2.5 | 1.0 | 367 | 800 + j7770 | 745 + j782 | 1360 + j12600 | 1240 + j1250 | 6 | 20 | 30 |
| 18CT6d | 60 | 90 | 78 | 0.017 | 0.45 | 2140 | 57.3 | 18.0 | 1.0 | 1030 | 1050 + j3280 | 1880 + j611 | 1690 + j4800 | 2830 + j848 | 6 | 25 | 45 |
| 23CT4c | 400 | 90 | 78 | 0.0057 | 0.071 | 730 | 57.3 | 2.0 | 1.0 | 330 | 750 + j8570 | 660 + j812 | 1230 + j14300 | 1100 + j1360 | 6 | 20 | 45 |
| 23CT6d | 60 | 90 | 78 | 0.0185 | 0.5 | 1830 | 57.3 | 14.0 | 1.0 | 800 | 883 + j3080 | 1500 + j512 | 1380 + j4790 | 2370 + j791 | 6 | 30 | 45 |
For a CT the 3-wire stator is the excited winding and the rotor is the output, so “Rated V” is the stator L-L voltage and “No-load output V” is the rotor voltage. The DC-resistance columns keep the source table’s rotor/stator order.
Synchro Control Differential Transmitters (CDX)
| Type | Freq (Hz) | Rated V | No-load input V | No-load input A (max) | No-load input W (max) | Rotor DC R (Ω) | No-load output V | Phase lead (°) | Stator DC R (Ω) | Zro (Ω) | Zrs (Ω) | Zso (Ω) | Zss (Ω) | Stator error (arc-min) | Rotor error (arc-min) | Residual fund. (mV) | Residual total (mV) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26V 08CDX4(B1) | 400 | 11.8 | 10.2 | 0.200 | 0.800 | 19 | 11.8 | 13.0 | 34 | — | — | 20 + j56 | — | 10 | 10 | 30 | 60 |
| 26V 08CDX4c | 400 | 11.8 | 10.2 | 0.108 | 0.300 | 24 | 11.8 | 9.5 | 36 | 33 + j124 | 46 + j14 | 24 + j108 | 39 + j14 | 7 | 7 | 20 | 30 |
| 26V 11CDX4c | 400 | 11.8 | 10.2 | 0.150 | 0.340 | 10.6 | 11.8 | 5.7 | 16.6 | 17.6 + j86 | 20.7 + j8.7 | 12.2 + j75 | 17.5 + j8.5 | 7 | 7 | 17 | 26 |
| 11CDX4b | 400 | 90 | 78 | 0.049 | 0.730 | 191 | 90 | 4.7 | 446 | 450 + j1930 | 487 + j200 | 242 + j1690 | 421 + j211 | 7 | 7 | 60 | 90 |
| 15CDX4d | 400 | 90 | 78 | 0.090 | 1.340 | 10 | 90 | 5.2 | 139 | 159 + j1060 | 190 + j125 | 129 + j917 | 164 + j111 | 6 | 6 | 32 | 60 |
| 15CDX6c | 60 | 90 | 78 | 0.038 | 0.630 | 515 | 90 | 10.0 | 960 | 780 + j2625 | 1114 + j2270 | 435 + j2270 | 930 + j880 | 7 | 7 | 60 | 100 |
| 18CDX4c | 400 | 90 | 78 | 0.128 | 1.210 | 47 | 90 | 3.0 | 46 | 65 + j669 | 72 + j71 | 63 + j623 | 65 + j64 | 6 | 6 | 40 | 75 |
| 18CDX6d | 60 | 90 | 78 | 0.052 | 1.450 | 599 | 90 | 17.0 | 897 | 717 + j1850 | 1130 + j315 | 465 + j1490 | 885 + j308 | 7 | 7 | 60 | 100 |
| 23CDX4c | 400 | 90 | 78 | 0.285 | 2.900 | 18 | 90 | 3.0 | 19 | 26 + j310 | 27 + j30 | 24 + j280 | 24.7 + j27.2 | 7 | 7 | 30 | 60 |
| 23CDX6c | 60 | 90 | 78 | 0.090 | 1.820 | 255 | 90 | 11.0 | 315 | — | 453 + j147 | 214 + j947 | — | 8 | 8 | 40 | 65 |
Synchro Torque Transmitters (TX)
| Type | Freq (Hz) | Rated V | No-load input V | No-load input A (max) | No-load input W (max) | Rotor DC R (Ω) | No-load output V | Phase lead (°) | Stator DC R (Ω) | Zro (Ω) | Zrs (Ω) | Zso (Ω) | Zss (Ω) | Stator error (arc-min) | Residual fund. (mV) | Residual total (mV) | Min. torque gradient (g·cm/°) | Max. continuous torque (g·cm) | Displacement at max. torque (°) | Pull-out torque (g·cm) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26V 11TX4c | 400 | 26 | 26 | 0.280 | 1.00 | 7.8 | 11.8 | 3.8 * | 2.8 | 13.7 + j114 | 19.4 + j8.7 | 3.1 + j19.4 | 3.3 + j1.3 | 7 | — | — | 0.55 | 25 | 38 | 40 |
| 11TX4b | 400 | 115 | 115 | 0.060 | 1.08 | 163 | 90 | 6 | 148 | 285 + j2140 | 370 + j159 | 175 + j1090 | 191 + j76 | 7 | — | — | 0.61 | 25 | 38 | 40 |
| 15TX4b | 400 | 115 | 115 | 0.200 | 3.10 | 37.5 | 90 | 2.5 | 40 | 100 + j955 | 96 + j68 | 65 + j493 | 48 + j33 | 6 | 120 | 220 | 2.2 | 22 | 10 | 85 |
| 18TX6a | 60 | 115 | 115 | 0.105 | 4.00 | 245 | 90 | 14 | 300 | 335 + j1270 | 686 + j210 | 256 + j916 | 379 + j81 | 6 | — | — | 3.6 | 134 | 37 | 172 |
| 23TX4b | 400 | 115 | 115 | 0.719 | 6.50 | 2.3 | 90 | 1 | 2.6 | 15.5 + j192 | 10.8 + j10.6 | 7.5 + j98 | 5.1 + j5.0 | 6 | — | — | 18 | 290 | 16 | 1380 |
| 23TX6b | 60 | 115 | 115 | 0.230 | 6.00 | 75 | 90 | 7 | 103 | 96 + j738 | 210 + j63 | 78 + j445 | 106 + j24 | 8 | — | — | 8.6 | 475 | 44 | 700 |
* Printed as “38” in the source scan; 3.8° is assumed because the electrically identical 26V 11TR4b row below reads 3.8.
Synchro Torque Receivers (TR)
| Type | Freq (Hz) | Rated V | No-load input V | No-load input A (max) | No-load input W (max) | Rotor DC R (Ω) | No-load output V | Phase lead (°) | Stator DC R (Ω) | Zro (Ω) | Zrs (Ω) | Zso (Ω) | Zss (Ω) | Stator error (arc-min) | Receiver error (arc-min) | Min. torque gradient (g·cm/°) | Max. continuous torque (g·cm) | Displacement at max. torque (°) | Pull-out torque (g·cm) | Synchronizing time, 30° (s) | Synchronizing time, 175° (s) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26V 11TR4b | 400 | 26 | 26 | 0.280 | 1.10 | 7.8 | 11.8 | 3.8 | 2.8 | 13.7 + j114 | 19.4 + j8.7 | 3.1 + j19.4 | 3.3 + j1.3 | 7 | 60 | 0.61 | 25 | 38 | 40 | 1.5 | 2.5 |
| 11TR4h | 400 | 115 | 115 | 0.060 | 1.08 | 163 | 90 | 6.0 | 148 | 285 + j2140 | 370 + j159 | 175 + j1090 | 191 + j76 | 7 | 60 | 0.61 | 25 | 38 | 40 | 1.5 | 2.5 |
| 15TR4c | 400 | 115 | 115 | 0.190 | 3.40 | 37.5 | 90 | 2.5 | 40 | 100 + j995 | 96 + j68 | 65 + j493 | 44 + j33 | 6 | 45 | 2.20 | 22 | 10 | 85 | 1 | 2 |
| 15TR6a | 60 | 115 | 115 | 0.200 | 3.10 | 400 | 90 | 13.0 | 340 | 502 + j2240 | 885 + j194 | 301 + j1400 | 509 + j106 | 6 | 45 | 2.20 | 70 | 33 | 95 | 1 | 2 |
| 18TR4h | 400 | 115 | 115 | 0.430 | 4.00 | 9.5 | 90 | 1.5 | 10.5 | 25 + j370 | 25 + j25 | 16 + j180 | 12 + j12 | 5 | 45 | 7.20 | 104 | 12 | 455 | 1 | 2 |
| 23TR4b | 400 | 115 | 115 | 0.719 | 6.50 | 2.3 | 90 | 1.0 | 2.6 | 15.5 + j192 | 10.8 + j10.6 | 7.5 + j98 | 5.1 + j5.0 | 6 | 45 | 18.00 | 290 | 16 | 1380 | 1 | 2 |
Torque receivers have much lower Zso than control transformers of the same size, which is why driving a TR directly from a D/S needs the high-power channel variants (see the DS MODULE GUIDE). The complete Appendix A, together with Chapter 4’s tables of resolver control-transformer impedances (Fig. 4-26), is available as a PDF from naii.com Application Notes → Instruments (login required).