APPLICATION NOTE 4247

Oscillator Design Considerations for Low-Current Applications


Abstract: This application note describes how low-frequency oscillator design and crystal selection affect operating current. When running the oscillator from a limited-capacity supply, such as a lithium coin cell or super capacitor, minimizing the operating current increases the operating time.

Introduction

Maxim has a large portfolio of low-power, battery-backed real-time clocks (RTCs). A primary consideration when Maxim designs an RTC is minimizing the power requirements of the oscillator when the RTC is running from the backup supply, so as to maximize the life of the backup source. Crystal oscillators provide reasonable accuracy, and development efforts for many years have focused on minimizing power consumption.

Oscillator design goals include the following:
  • Provide enough current and gain to start and maintain oscillation
  • Provide a wide operating-voltage range
  • Minimize the influence of external noise on accuracy

Key Crystal and Oscillator Parameters

Figure 1 presents an equivalent circuit of a crystal resonator. A crystal has two frequencies of zero phase, as shown in Figure 2. The lower frequency is the series resonant frequency. At the series resonant frequency, L1 and C1 cancel, and the impedance is determined by R1.¹ The second, higher, frequency is the parallel resonant frequency. At parallel resonance, resistance is at a maximum.

A parallel resonant oscillator circuit (Figure 3) uses a crystal that is designed to operate with a specified load capacitance. This results in a circuit that operates at a frequency between the series resonant point and the parallel resonant point. A change in the load capacitance causes a change in the oscillator frequency.

Crystal equivalent series resistance (ESR) tends to shift upwards after going through SMT reflow, so an SMT crystal that is otherwise similar to a through-hole package crystal may have a higher maximum ESR specification. Likewise, smaller tuning-fork crystals will usually have higher ESR specifications than larger ones.

Figure 1. Equivalent circuit of a crystal resonator.
Figure 1. Equivalent circuit of a crystal resonator.

Figure 2. Crystal phase and impedance response.
Figure 2. Crystal phase and impedance response.

Figure 3. Pierce-type (inverter variation) oscillator circuit.
Figure 3. Pierce-type (inverter variation) oscillator circuit.

Oscillator Current

As Eric Vittoz has observed, when both load capacitors in a crystal oscillator circuit (Figure 3) are of equal value, the minimum current for oscillation (or critical transconductance) can be approximated by the equation below.²

gmcrit ≈ 4ω² × CL² × RESR (Eq. 1)
Where ω is the frequency in radians, CL is the equivalent capacitive load, and RESR is the ESR of the crystal. The oscillator is assumed to be a CMOS device operating in weak inversion.

Vittoz also determines that the oscillator amplitude and bias current are related by the following equation:
Equation 2. (Eq. 2)
Where Equation 3. and IB0 and IB1 are zero- and first-order modified Bessel functions.

We can therefore show the relationship between oscillator current at a given oscillator voltage with different values of ESR and CL, as shown in the following example. Assuming that V1 = 400mVP-P, nUT = 26mV, ESR = 35kΩ, and CL = 6pF, then Equation 4. ≈ 4, and
IO ≈ 4ω² × CL² × RESR × nUT × 4
≈ 4 × (32,768 × 6.283)² × (6e-12)² × 35e+3 × 0.026 × 4
≈ 22.2nA.

Table 1 shows the relationship between both CL and ESR on oscillator current, using the values for V1 and nUT above.

Table 1. Crystal ESR and CL versus Oscillator Current
ESR (Ω) CL (pF) IO (nA)
35,000 6 22.2
70,000 6 44.4
35,000 12.5 88.9
70,000 12.5 177.8

Since in the equation for gmcrit the CL term is squared, doubling the load capacitance has the effect of increasing oscillator current by four times. Increasing the crystal ESR by two times causes the required oscillator current to double. Note that this is the minimum estimated oscillator current, which does not include current consumed by additional circuits for amplifying the oscillator output, nor does it include currents in the devices used to divide the frequency down to 1Hz.

Oscillator Design Requirements

An oscillator should be designed so that it has sufficient gain to operate over the entire operating temperature and voltage range. The amplitude must always be sufficient to drive the following gain and buffer stages under operating conditions. To minimize oscillator current requirements, for a given oscillation voltage, a low CL is desired. Lower CL, however, will increase an oscillator's susceptibility to the influence of external noise. Poor availability of low CL crystals may make selection of a crystal with a higher CL necessary, at the cost of increased oscillator current. Likewise, if a design requires a small crystal package, an oscillator design that will drive a high ESR crystal is needed, increasing the necessary oscillator current.

Additionally, circuits used to add desirable functions, such as glitch filters to improve oscillator noise immunity, or circuits to detect when the oscillator has stopped, will add to the circuit's overall current consumption.³

Conclusion

There are a number of tradeoffs to be considered when designing an oscillator for a low-power RTC. Increasing CL will increase noise immunity and may provide a larger selection of crystal models to choose from, at the expense of oscillator current. Likewise, designing an oscillator so that it will run with relatively high ESR crystals requires higher oscillator currents. Adding a glitch filter or oscillator stop detection circuit also adds beneficial functions, but draws additional current.



References
  1. Ecliptek Corporation, "Glossary of Terms for Crystals," www.ecliptek.com.
  2. Eric A. Vittoz, "High-Performance Crystal Oscillator Circuits: Theory and Application," IEEE Journal of Solid-State Circuits, Vol. 23, No. 3 (June 1988).
  3. See the Oscillator Stop Flag (OSF) bit description in the DS1337, DS1338, DS1339, DS1340, DS1341, DS1388, DS1390/91/92/93, and DS1318 data sheets.


Related Parts
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DS12R885 RTCs with Constant-Voltage Trickle Charger Free Samples  
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DS1305 Serial Alarm Real-Time Clock Free Samples  
DS1306 Serial Alarm Real-Time Clock Free Samples  
DS1307 64 x 8, Serial, I²C Real-Time Clock Free Samples  
DS1308 Low-Current I²C RTC with 56-Byte NV RAM Free Samples  
DS1315 Phantom Time Chip Free Samples  
DS1318 Parallel-Interface Elapsed Time Counter Free Samples  
DS1337 I²C Serial Real-Time Clock Free Samples  
DS1337 I²C Serial Real-Time Clock Free Samples  
DS1338 I²C RTC with 56-Byte NV RAM Free Samples  
DS1339 I²C Serial Real-Time Clock Free Samples  
DS1339 I²C Serial Real-Time Clock Free Samples  
DS1339A Low-Current, I²C, Serial Real-Time Clock Free Samples  
DS1339B Low-Current, I2C, Serial Real-Time Clock for High-ESR Crystals Free Samples  
DS1340 I²C RTC with Trickle Charger Free Samples  
DS1341 Low-Current I²C RTCs for High-ESR Crystals Free Samples  
DS1342 Low-Current I²C RTCs for High-ESR Crystals Free Samples  
DS1343 Low-Current SPI/3-Wire RTCs Free Samples  
DS1344 Low-Current SPI/3-Wire RTCs Free Samples  
DS1371 I²C, 32-Bit Binary Counter Watchdog Clock Free Samples  
DS1374 I²C, 32-Bit Binary Counter Watchdog RTC with Trickle Charger and Reset Input/Output Free Samples  
DS1388 I²C RTC/Supervisor with Trickle Charger and 512 Bytes EEPROM Free Samples  
DS1390 Low-Voltage SPI/3-Wire RTCs with Trickle Charger Free Samples  
DS1391 Low-Voltage SPI/3-Wire RTCs with Trickle Charger Free Samples  
DS1392 Low-Voltage SPI/3-Wire RTCs with Trickle Charger Free Samples  
DS1393 Low-Voltage SPI/3-Wire RTCs with Trickle Charger Free Samples  
DS1500 Y2K-Compliant Watchdog RTC with NV Control  
DS1501 Y2K-Compliant Watchdog Real-Time Clocks Free Samples  
DS1558 Watchdog Clocks with NV RAM Control Free Samples  
DS1670 Portable System Controller Free Samples  
DS1672 I²C 32-Bit Binary Counter RTC Free Samples  
DS1673 Portable System Controller Free Samples  
DS1677 Portable System Controller Free Samples  
DS1678 Real-Time Event Recorder Free Samples  
DS1678 Real-Time Event Recorder Free Samples  
DS1685 3V/5V Real-Time Clock Free Samples  
DS17285 3V/5V Real-Time Clocks Free Samples  
DS17485 3V/5V Real-Time Clocks Free Samples  
DS17885 3V/5V Real-Time Clocks Free Samples  


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© Jan 26, 2011, Maxim Integrated Products, Inc.
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APP 4247: Jan 26, 2011
APPLICATION NOTE 4247, AN4247, AN 4247, APP4247, Appnote4247, Appnote 4247