Read e-book online A K -automorphism with non-isomorphic ZxZ2 actions PDF

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Additional resources for A K -automorphism with non-isomorphic ZxZ2 actions

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Some of the older op amps must limit their transfer equation as shown in Equation 4–7. V OUT + ǒV CC * V INǓ RF RG for V OH w V OUT w V OL (4–7) The noninverting op amp circuit is shown in Figure 4–8. Equation 4–8 is written with the aid of superposition, and simplified algebraically, to acquire Equation 4–9. V OUT + V IN ǒ Ǔǒ RF RG ) RF V OUT + ǒV IN–V REFǓ Ǔ RF ) RG R * V REF F RG RG RF RG (4–8) (4–9) RF , there are two possible circuit solutions. First, when VIN RG is a negative voltage, VOUT must be a negative voltage.

These capacitors are called decoupling capacitors, and they are included to reduce noise and provide increased noise immunity. 01-µF capacitors serve this purpose, sometimes more extensive filtering is needed, and sometimes one capacitor serves this purpose. Special attention must be paid to the regulation and noise content of VCC when VCC is used as a reference because some portion of the noise content of VCC will be multiplied by the circuit gain. 01 µF RF VREF RG RL Figure 4–10. Schematic for Case1: VOUT = +mVIN + b The circuit equation is written using the voltage divider rule and superposition.

3)m ) b (4–60) From these equations we find that b = –1 and m = –20. Setting the magnitude of m equal to Equation 4–57 yields Equation 4–61. |m| + 20 + RF R G1 (4–61) R F + 20R G1 (4–62) Let RG1 = 1 kΩ, and then RF = 20 kΩ. 2 (4–64) |b| + V CC R G2 + RF RF +5 +1 R G1 R G2 The final equation for this example is given in Equation 4–63. V OUT + –20V IN * 1 (4–65) The final circuit is shown in Figure 4–20 and the measured transfer curve for this circuit is shown in Figure 4–21. 01 µF Figure 4–20. 35 0 1 2 3 4 5 6 VOUT – Output Voltage – V Figure 4–21.

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A K -automorphism with non-isomorphic ZxZ2 actions by Park K.


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