ECRI Microelectronics

Design of a linear rotary transformer/digital to synchro/resolver converter

Design of a linear rotary transformer/digital to synchro/resolver converter
Abstract: Linear rotary transformers are widely used in solving quantities and high-precision servo systems due to their high precision and strong anti-interference ability. There are many technical solutions for realizing linear resolver solving circuit. This paper elaborates a conversion circuit design method based on DDC RD-19230 as the core chip, focusing on the design process and verifying the accuracy of the design method through experiments. .
Keywords: linear rotary transformer, RD-19230, digital to synchro/resolver converter

1 Introduction
    A rotary transformer is a control motor with a very detailed structure and manufacturing process, and its precision is high. The resolver is mainly divided into two types: a sine and cosine rotary transformer and a linear rotary transformer. The output voltage of the sine and cosine rotary transformer is sinusoidal or cosine-like. It is mainly used in the occasions of coordinate transformation and trigonometric calculation. The linear rotary transformer output voltage is linear with the rotation angle and is mainly used in applications where the rotation angle is required to be converted into an electrical signal. The linear rotary transformer makes the output voltage of the rotor linear with the rotor angle , so it can only be used as a linear transformation of mechanical angle and electrical signal within a certain angle of rotation.
    This paper introduces the basic structure and working principle of linear rotary transformer based on the perspective of the application. By analyzing the functional characteristics and internal structure of the tracking type conversion chip RD-19230, a linear rotary transformer digital to synchro/resolver converter is designed.
2 circuit design principle
2.1 Linear rotary transformer working principle
    A linear rotary transformer is a kind of rotary transformer whose output voltage is linearly related to the rotor rotation angle within a certain working angle range. The schematic diagram of the primary side compensation linear rotary transformer is listed below.

Figure 1 linear rotation and transformation principle diagram
    When the Z3Z4-winding of the linear resolver shown in Figure 1 is open, the excitation winding and the cosine winding are connected in series to the current source U, and a current flows through the two windings to generate Bj and Bc, respectively. The magnetic density Bj is true uranium magnetic, and Bc may be a direct axis component Bcd and a cross axis component Bcq, respectively. Since the compensation winding is short-circuited as the primary side compensation, it can be considered that the cross-axis component magnetic density Bcq is completely compensated, so there is no cross-axis magnetic field in the air gap. At this time, there is only a synthetic direct-axis magnetic flux Ф∑d in the resolver, which is only generated by the direct uranium magnetic field synthesized by Bj and Bcd. The direct-axis magnetic fluxФ∑d is respectively coupled to the field winding, the positive and the cosine output windings, and generates induced potentials Ej, Ec, and Es, respectively. These potentials are in phase in time, respectively
                               (1-1)
                          (1-2)
                           (1-3)
    If the impedance drop in the winding is ignored, then
        (1-4)
 When, then:
                                 (1-5)
When (1-5) is connected with (1-4)
                                        (1-6)
According to Equation 1-6, in Figure 2, Ku is 0.14, 0.46, 0.52, 0.67, and 0.95, the input voltage amplitude is 5V, and θ is changed from -180° to 180°, and the output voltage amplitude is changed. It can be seen that when Ku=0.52~0.67, the linearity of the rotary transformer at θ-[60°~60°] is better; while at Ku=0.97, the linearity characteristic is obviously deteriorated.

Figure 2 line performance to transformer B output
In the actual linear rotary transformer, in order to obtain the best linear characteristics, when the internal resistance of the power supply is small, the ratio of Ku is generally 0.56 to 0.57.
2.2 Design method for realizing linear rotary transformer/digital conversion 
With the development of modern electronic technology, people have put forward higher requirements on the conversion precision, conversion speed and reliability, structure and price of the shaft angle digital to synchro/resolver converter. Based on the current status quo, linear resolver/digital conversion is realized mainly through tracking conversion, digitization and other conversion schemes. Among them, the digital linear rotary transformer/digital circuit has the disadvantages of long development cycle and low precision. The tracking type conversion scheme has the characteristics of strong anti-interference ability and strong real-time performance. Therefore, most linear resolver digital conversion adopts this scheme.
In this paper, the II-type servo tracking principle is used to design the circuit. The two-wire AC voltage output from the linear rotary transformer is converted by the tracking type conversion chip RD-19230, and the 12-bit parallel binary digital quantity is output. Its digital output automatically tracks the shaft angle input at the selected maximum tracking rate with no static errors.
2.3 RD-19230 chip working principle
The RD-19230 is a mixed-signal CMDS IC that includes an analog input digital output section. The precision analog circuitry is combined with digital logic to form a complete high-performance tracking analog-to-digital converter. Its main operating characteristics and parameters are as follows: +5V single power supply; internal charge pump to provide -5V power supply for external; conversion accuracy up to 1.3 cents; programmable resolution, bandwidth and tracking speed; with internal integrated reference ; can replace the speed output of the tachometer; parallel data output, output programmable latch; programmable LVDT mode; normal operation in the temperature range of -40 ~ +85 °C.

Figure 3 RD-19230 block diagram
Figure 3 shows the internal block diagram of the RD-19230. The principle uses a Type II servo loop, and its output digital quantity continuously tracks the change of the input voltage continuously. The high-precision proportional bridge inside the block diagram compares the input reference signal with the input signal and compares it with the digital data Φ of the reversible counter to obtain the data of the AC error phase-sensitive demodulation, integral error processing, and VCO correction reversible counter. Until θ-Φ tends to 0, so that the input signal ratio corresponds to θ.
2.4 offset binary code
Converting positive and negative data is often referred to as bipolar work. There are many methods for expressing digital quantities in a computer as bipolar, such as original code, complement, inverse code, and binary code. Among them, the complement and offset binary codes are mainly used for D/A converters. The RD-19230 chip uses the RVDT mode to transmit the digital method as a parallel offset binary code. The offset binary code is described below.
The offset binary code (also called the frame shift code) is an offset binary code of the alpha bit binary number ±D obtained by adding an offset to the binary code as:

2n in the equation is the offset. For example, if a 3-bit binary number Di=+110, then its corresponding offset binary code is:

A 3-bit binary number Di=-110, then its corresponding offset binary code is:

3. Circuit design
3.1 input signal conditioning circuit
The internal processing signal of the RD-19230 chip is two orthogonal signals. Normally, it can be directly supplied by the resolver. Under normal working conditions, the voltage requirements of the two input signals are 2mg±15%, and the output signal of the linear rotary transformer is two lines. It is necessary to design a simple and convenient conversion circuit.
With different types of linear resolvers, the reference and signal voltages are different. Therefore, it is necessary to convert the input signal into a standard signal RD-19230 chip signal that can be recognized by the RD-19230 through a specific signal conditioning circuit. An operational amplifier is present inside the input, which simplifies the circuit and makes the circuit application more convenient.

Figure 4 linear rotary transformer input signal proportional conversion circuit
V1 point setting voltage requirement: 
V2 point setting voltage requirement: 
It can be seen from Fig. 4 that the SIN signal voltage is (VA+VB)/2 and the cos signal voltage is (VB-VA)/2. C1 and C2 are compensated phases and are set according to the characteristics of the linear resolver used.
Taking the linear rotary transformer 36XX6-1 as an example, the rated voltage is 30Vrms, the operating frequency is 40Hz, and the transformation ratio is 0.58. The maximum signal of 17.4 Vrms is calculated from the ratio. Normally, the linear rotary transformer is a linear segment between -60° and 60°. In order to facilitate system control, the over-full input threshold can be set according to the input angle. This circuit design uses the value of 80° as the full scale value. It will be proportional, rated voltage, sin80 ° and cos80 °. Substituting into Equations 1-6, it can be concluded that the signal voltage corresponding to 80° is 15.568 Vrms. Therefore, the proportional resistance of Va is set to R=135KΩ and aR=18KΩ, and the proportional resistances R=135KΩ and bR=9KΩ are set, so that when the input angle is 80°, the output corresponds to the offset binary code full scale value.
3.2 working mode setting
The RD-19230 chip sets the resolution and operating mode through D0 and D1. In this paper, D0 is connected to -5V, D1 is connected to +5V, and it is set to LVDT mode with a resolution of 12 bits. In order to reduce the input power type and power conversion circuit, the internal output of the RD-19230 chip is usually used to connect -5V to D0. However, when using the internal -5V output, the RD-19230 chip speed signal voltage will be limited to 3.5V, which will affect the tracking rate calculation. Figure 5 shows an external connection using the internal -5V of the chip. Pins 27, 58, and 33 are connected together to +5V DC; pins 16, 17 and 23 are connected together to output -5V, and as shown, 47uF and 10uF decoupling capacitors are placed at the root of the device.

Figure 5-5 Conversion circuit settings
3.2 resolution setting and weight table
When the RD-19230 chip is operating in LVDT mode, the first bit and the second bit are overfilled, the third bit is the MSB, and the resolution is 8, 10, 12, and 14 bits programmable. The output mode uses parallel offset binary. According to the input signal conditioning circuit angle setting, the corresponding relationship between the 12-bit output code and the input angle of this circuit is shown in Table 1.
Table 1 12-bit output code
angular Output(Over1、 Over2 、MSB-LSB)
80° 01 1111 1111 1111
60° 00 1110 0001 0011
00 1000 0000 0000
-60° 00 0001 1111 0100
-80° 11 0000 0000 0000
According to the linear resolver input signal, Table 2 lists the 12-bit resolution linear resolver input signal weight table. The weight is calculated as follows
Bit3:0.5/0.5=1 Arc Tan(1)=45°
Bit4:0.25/0.75=0.333 Arc Tan(0.333)=18.435°
Bit5:0.125/0.875=0.143 Arc Tan(0.143)=8.130°
Table 2 weight table
BIT angular
3 45°
4 18.435°
5 8.130°
6 3.814°
7 1.848°
8 0.911°
9 0.451°
10 0.225°
11 0.122°
12 0.056°
3.3 setting of closed loop parameters
The design of the RD-19230 peripheral circuit is shown in Figure 3. Its peripheral circuits are composed of ordinary resistors and capacitors, and their accuracy is not excessively high. Some important performance indicators of the system, such as system bandwidth and maximum tracking rate, can be set by the user according to actual needs. The following describes the parameter design of each part according to the function.
Firstly, determine the working frequency of the design product f=400Hz, and select the appropriate bandwidth f according to the working frequency f≥F. Second, the tracking rate is determined by setting the RSET and RCLK resistors. Referring to the RD-19230 device PDF, the resistance value is chosen to be 30K, which means that at 12-bit resolution, the maximum tracking rate is 288 rpm. The same setting can be achieved without the resistor RSET being connected, but in contrast, if a high precision resistor is used, the output voltage has better temperature characteristics. Finally, calculate the remaining resistance parameters.
Among them, F represents the internal sampling frequency, which needs to be determined according to the resistance value of RCLK. The smaller the resistance value, the higher the internal counting frequency. Refer to the RD-19230 device PDF when RCLK = 30KΩ, F = 67kHz. According to the design requirements, determine the tracking rate that needs to be designed. According to the above formula, the specific parameters of RV、CBW 、RB 、RB/10 can be calculated in turn.
3.4 Dynamic performance analysis
The transfer function block diagram of the converter designed with RD-19230 chip is shown in Figure 6. It can be seen that the circuit includes two pure integral links and is a typical second-order non-stationary system. Therefore, the converter's angle input to the step or uniform ramp is not purely in the steady-state conversion error, and there is a principle conversion error for the angle of acceleration, which is inversely proportional to the open-loop gain of the system.
Open loop transfer function 
Once the loop parameters RV、CBW 、RB are determined, the formula for calculating A1 and 
Among them, Cs is 10PF, Cvco is 50PF, gain coefficient A=A1*A2, A1 is the integrator gain, and A2 is the VCO gain. Each LSB error gain (including proportional bridge slope, error amplifier amplification, phase sensitive demodulation) is 0.011. It can be seen that the system gain is mainly the product of LSB error gain, integrator gain and VCO gain. The gain factor A of this circuit design is 15700/S2.
3 Test results
According to the above design, a MLRDC4714-41-30/17 linear resolver/digital converter was developed. The technical indicators reached by the product are shown in Table 3. It can be seen from the test results that the product has the characteristics of high conversion precision and low power consumption. Therefore, the design is reasonable and feasible.
Table 3 main technical indicators of the product,
Features symbol Actual value
Resolution ratio RES 12bit
Output bit D 14bit
Linearity ERL 0.085%
Conversion accuracy r 2LSB
repeatability θR 1LSB
Signal input impedance Zi 140.1KΩ
Reference input impedance Zo 137.7KΩ
Output high reference level VOH 4.996V
Output low reference level VOL 0.03V
Power dissipation PD 0.92W

4 Conclusions
In this paper, by analyzing the working mechanism of linear rotary transformer, the design method of RD-19230 in linear rotary transformer/digital conversion is proposed. The main parameters design and theoretical calculation of the circuit are given. The products made by this development scheme have the characteristics of high output precision and good dynamic characteristics, and can be widely applied to products such as angle measurement and automatic control.

References:
[1] RD/RDC Series Converters Applications Manual M] Data Devices Corporation, 1998.
[2] Data Devices Corporation. Data Converter Reference Manual Volume I [MI. USA, 1999
[3] Data Device Corporation 16 bit monolithic tracking resolver-to-digital converter [M].1999
4] Zhang Weisheng et al. Design of Angle Measuring and Control Device Based on Linear Resolver, Automation Instrumentation, Vol. 23, No. 10, October 2002
[5] Lv Yunfeng et al. Design of interface circuit for self-aligning machine based on RD-19230, Electronic Design Engineering, No. 19, No. 6, March 2011
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