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Use of the CMOS Unbuffered Inverter in Oscillator Circuits Application Report SZZA043 - January 2004 Use of the CMOS Unbuffered Inverter in Oscillator Circuits Moshiul Haque and Ernest Cox Standard Linear & Logic ABSTRACT CMOS devices have a high input impedance, high gain, and high bandwidth. These characteristics are similar to ideal amplifier characteristics and, hence, a CMOS buffer or inverter can be used in an oscillator circuit in conjunction with other passive components. Now, CMOS oscillator circuits are widely used in high-speed applications because they are economical, easy to use, and take significantly less space than a conventional oscillator. Among the CMOS devices, the unbuffered inverter (’U04) is widely used in oscillator applications. This application report discusses the performance of some TI ’U04 devices in a typical crystal-oscillator circuit. Contents 1 Introduction . 3 2 Theory of Oscillators . 3 2.1 Characteristics of Crystals. 3 3 Buffered and Unbuffered CMOS Inverters in Oscillator Circuits. 6 4 Characteristics of a CMOS Unbuffered Inverter. 7 4.1 Open-Loop Gain . 7 4.2 VO vs VI . 8 4.3 ICC vs VI . 9 4.4 Variation of Duty Cycle With Temperature. 10 5 Characteristics of LVC1404. 11 6 Practical Oscillator Circuits. 12 6.1 Selection of Resistors and Capacitors. 13 6.1.1 RF . 13 6.1.2 RS . 13 6.1.3 C1 and C2 . 16 7 Practical Design Tips . 16 Appendix A. Laboratory Setup. 18 A.1 Laboratory Setup to Measure Open-Loop-Gain Characteristics. 18 A.2 Laboratory Setup to Measure ICC vs VI Characteristics. 18 Appendix B. LVC1GU04 in Crystal-Oscillator Applications. 19 B.1 LVC1GU04 in 25-MHz Crystal-Oscillator Circuit. 19 B.2 LVC1GU04 in 10-MHz Crystal-Oscillator Circuit. 20 B.3 LVC1GU04 in 2-MHz Crystal-Oscillator Circuit. 21 B.4 LVC1GU04 in 100-kHz Crystal-Oscillator Circuit. 22 Trademarks are the property of their respective owners. 1 SZZA043 Appendix C. LVC1404 in Crystal-Oscillator Applications. 23 C.1 LVC1404 in 25-MHz Crystal-Oscillator Circuit. 23 C.2 LVC1404 in 100-kHz Crystal-Oscillator Circuit. 24 List of Figures 1 Oscillator . 3 2 Electrical-Equivalent Circuit of a Crystal. 4 3 Pierce Oscillator Using CMOS Inverter. 5 4 Open-Loop-Gain Characteristics of LVC1GU04. 6 5 Open-Loop-Gain Characteristics of AHC1GU04. 6 6 Open-Loop-Gain Characteristics of AUC1GU04. 7 7VO vs VI Characteristics of LVC1GU04. 7 8VO vs VI characteristics of AHC1GU04. 8 9VO vs VI Characteristics of AUC1GU04. 8 10 ICC vs VI Characteristics of LVC1GU04. 8 11 ICC vs VI Characteristics of AHC1GU04. 10 12 ICC vs VI Characteristics of AUC1GU04. 10 13 Duty-Cycle Variation in LVC1GU04. 10 14 Duty-Cycle Variation in AHC1GU04. 11 15 Duty−Cycle Variation in AUC1GU04. 11 16 Pinout Diagram for LVC1404. 11 17 Logic Diagram of LVC1404. 12 18 Open-Loop-Gain Characteristics of LVC1404. 12 19 Pierce Oscillator Circuit Using Unbuffered CMOS Inverter. 13 20 Effect of RS on Oscillator Waveform (No Load). 14 21 Effect of RS on Oscillator Waveform (RL = 1 kW)14. 22 Effect of RS on the Frequency Response of Feedback Network. 15 23 Effect of RS on the Phase Response of Feedback Network. 15 24 Oscillator Circuit Using a Schmitt-Trigger Input Inverter. 17 A-1 Open-Loop-Gain Measurement Setup. 18 A-2 ICC vs VI Measurement Setup. 18 B-1 Effect of RS on Duty Cycle and ICC (Frequency = 25 MHz). 19 B-2 Effect of RS on Duty Cycle and ICC (Frequency = 10 MHz). 20 B-3 Effect of RS on Duty Cycle and ICC (Frequency = 2 MHz). 21 B-4 Effect of RS on Duty Cycle and ICC (Frequency = 100 kHz). 22 C-1 Output Waveform of Oscillator Circuit Using LVC1404 (Frequency = 25 MHz). 23 C-2 Output Waveform of Oscillator Circuit Using LVC1404 (Frequency = 100 kHz). 24 List of Tables B-1 Effect of RS on Duty Cycle and ICC (Frequency = 25 MHz). 19 B-2 Effect of RS on Duty Cycle and ICC (Frequency = 10 MHz). 20 B-3 Effect of RS on Duty Cycle and ICC (Frequency = 2 MHz). 21 B-4 Effect of RS on Duty Cycle and ICC (Frequency = 100 kHz). 22 2 Use of the CMOS Unbuffered Inverter in Oscillator Circuits SZZA043 1 Introduction Resistors, inductors, capacitors, and an amplifier with high gain are the basic components of an oscillator. In designing oscillators, instead of using discrete passive components (resistors, inductors, and capacitors), crystal oscillators are a better choice because of their excellent frequency stability and wide frequency range. A crystal basically is an RLC network that has a natural frequency of resonance. 2 Theory of Oscillators In principle, an oscillator can be composed of an amplifier, A, with voltage gain, a, and phase shift, α, and a feedback network, F, with transfer function, f, and phase shift, β (see Figure 1). V V 1 Amplifier, A 2 a, a Feedback Network, F f, b Figure 1. Oscillator For |f| |a| w 1 the oscillating condition is fulfilled, and the system works as an oscillator. f and a are complex quantities; consequently, it is possible to derive from equation 1 |f| |a| expƪjǒa ) bǓ w 1ƫ (1) the amplitude |f| |a| w 1 (2) and the phase ǒa ) bǓ + 2 p (3) To oscillate, these conditions of amplitude and phase must be met. These conditions are known as the Barkhausen criterion. The closed-loop gain should be ≥1, and the total phase shift of 360 degrees is to be provided. 2.1 Characteristics of Crystals Figure 2 is an electrical-equivalent circuit of a quartz crystal. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 3 SZZA043 C L R C0 Figure 2. Electrical-Equivalent Circuit of a Crystal The quantities C and L are determined by the mechanical characteristics of the crystal; R is the resistance of the resonant circuit at the series resonance, and Co represents the capacitance of the leads and electrodes. Co is much larger than C and is affected by the stray capacitances of the final circuit. Because R is negligible, the impedance of this circuit is given by equation 4. j w2 * Z + LC 1 (4) w ǒ 2 Ǔ (Co ) C) * w LCCo A series-resonance frequency is attained when the impedance, Z, approaches 0, Z → 0 1 f = ser 2p LC (5) A parallel-resonance frequency is attained when the impedance, Z, approaches ∞ , Z → ∞ = C fpar f ser 1 + Co (6) An oscillator circuit using the parallel resonance mode of the crystal is less.
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