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MC10E197FNR2 Arkusz danych(PDF) 9 Page - ON Semiconductor |
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MC10E197FNR2 Arkusz danych(HTML) 9 Page - ON Semiconductor |
9 / 16 page MC10E197 http://onsemi.com 9 Analysis of this portion of the filter circuit yields the transfer function: F1(s) = Kl * 1 s * (s + z) [s2 + (2ζω ) s + ω2 ]o2 o2 The gain constant is defined as: where: Al = op-amp gain constant for selected pole positions. RA = integrator feedback resistor. RlA = integrator input resistor. Kl = Al * RA RlA eqt. 5 The integrator circuit introduces a zero, a pole at the origin, and a second order pole set as described by the two pole model for an op-amp. As in the case of the differential summing amplifier, we assume the op-amp pole pair occur as a complex conjugate pair making an angle of 45° to the real axis of the complex frequency plane; are positioned for near unity gain operation; and are located beyond the crossover frequency. Since both the summing and integrating op-amps are realized by the same type of op-amp (MC34182D), the open loop pole positions for both amplifiers will be the same. Further, the loop transfer function contains two poles located at the origin, one introduced by the integrator and the other by the VCO; hence a zero is necessary to compensate for the phase shift produced by these poles and ensure loop stability. The op-amp will be stable if the crossover point occurs before the transfer function phase angle becomes 180°. The zero should be positioned much less than one decade before the unity gain frequency. As in the case of the filter input circuitry, the poles and zero from this analysis will be used as open loop poles and a zero when performing the root locus analysis for the complete system. Determination of Element Values The location of the zero is used to determine the element values for the augmenting integrator. The value of the capacitor, CA, is selected to provide adequate charge storage when the loop is not sampling data. A value of 0.1 μF is sufficient for most applications; this value may be increased when the RDCLK frequency is much lower than 4 MHz. The value of RA is governed by: ⎥ z⎥ = 1 2πRACA eqt. 6 For unity gain operation of the integrating op-amp the value of RlA is selected such that: RlA = RA eqt. 7 It should be noted that although the zero can be tuned by varying either RA or CA, caution must be exercised when adjusting the zero by varying CA because the integrator gain is also a function of CA. Further, the gain of the loop filter can be adjusted by changing the integrator input resistor RlA. Voltage Divider The input range to the VCOIN input is from 1.3 V + VEE to 2.6 V + VEE; hence, the output from the augmenting amplifier section must be attenuated to meet the VCOIN constraints. A simple voltage divider network provides the necessary attenuation (Figure 8). VIN RV RO DB Cd VO Figure 8. Voltage Divider Subsection In addition, a shunt filter capacitor connected between the VCOIN input pin and VEE provides the voltage divider subsection with a single time constant transfer function that adds a pole to the overall loop filter. The transfer function for the voltage divider network is: Fd(s) = Kd * 1 (s + p2) The gain constant, Kd, is defined as: Kd = 1 Rv Cd eqt. 9 he value of Kd is easily extracted by rearranging Equation 1: Kd = Kol Kφ * Ko * K1 * Kl eqt. 10 The gain constant Kd is set such that the output from the integrator circuit is within the range 1.3 V +VEE to 2.6 V +VEE. The pole for the voltage divider network should be positioned an octave beyond that for the filter input. Determination of Element Values Once the pole location and the gain constant Kd are established the resistor values for the voltage divider network are determined using the design guidelines mentioned above and from the following relationship: Kd 2π⎥ p2⎥ = Ro Ro + Rv Having determined the resistor values, the filter capacitor is calculated by rearranging Equation 9: Cd = 1 Rv Kd eqt. 9a Finally, a bias diode is included in the voltage divider network to provide temperature compensation. The finite resistance of this diode is neglected for these calculations. |
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Podobny opis - MC10E197FNR2 |
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