MERCURY Technical Note USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 No.: TN- 021 Revision: 0 Date: Jan. 10, 2001 Page 1 of 6 Title: The effect of load capacitor on the crystal Why load capacitor is needed In early days, crystal manufacturer needed the whole equipment or at least the oscillator section of the equipment from customers in order to correlate the oscillator frequency for that particular equipment. Later on, additional crystal parameters such as C1 (motional capacitance), L1 (motional inductance), Co (shunt capacitance) were introduced to define the crystal parameters. Crystal frequency is primarily determined by its C1 and L1 . Figure 1 shows the equivalent circuit of a crystal. Co is considered as an external load to the crystal. For more discussion of the crystal equivalent circuit please refer to Mercury technical note TN-011. From the equivalent circuit the resonant frequency can be expressed as 1 f = ---------------- Equation 1 2 π L1C1 It is clear from equation 1that infinite combinations of L1 and C1 can yield the same frequency. This suggests crystals of same frequency do not necessarily yield the same output frequency even for the same oscillator circuit. Different Co (for example crystals made different manufacturers) and/or loading variations from oscillators to oscillators can cause a wide spread of output frequency. To compromise all these variables, Load capacitor was then introduced to better describe a crystal in a circuit. Load capacitor go t its name because it is the capacitive load that the oscillator circuit loads onto the crystal or the capacitive load the crystal “sees” from the circuit. To ways to use the load capacitors Load capacitor (C L), connected with crystal either in series or in parallel, is normally used for 5 fine tune the oscillator output frequency. As shown in figure 1,2 and 3 the output frequency can be pulled upward from fr (series resonant frequency of the crystal) by series load capacitor or downward from fa (anti- resonant frequency of the crystal) by parallel load capacitor. The amount of pulling (pull sensitivity) is determined by the CL value and the capacitance ratio (Co/C 1 ) of the crystal. Crystal with series load capacitor In the case of series connection, the reactance part of the crystal is zero and the crystal acts like a pure resistor. Zero reactance means the oscillator loading does not exert much to the crystal. When order crystals for this type of circuit please specify the loading condition as “Series”. Mercury part number, use HC-49/U 10.000 MHz as an example, becomes H49-10.000-S. Advantage of series crystals is good frequency correlation between user and the manufacturer and among manufacturers as well. However, stability of an oscillator circuit using parallel resonant crystal (discussed below) seems to be more stable than that of a comparable series oscillator circuit using series crystal. MERCURY Technical Note Revision: 0 USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 No.: TN- 021 Date: Jan. 10, 2001 Page 2 of 6 Co Fig. 1: Crystal without load capacitor L1 C1 R1 CL Co Fig. 2: Crystal with series load capacitor L1 C1 fa fr frequency - reactance R1 - reactance + reactance C1 fa fr frequency R1 Co CL Fig. 3: Crystal with parallel load capacitor - reactance + reactance L1 + reactance Title: The effect of load capacitor on the crystal fa fr frequency MERCURY Technical Note Revision: 0 USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 No.: TN- 021 Date: Jan. 10, 2001 Page 3 of 6 Title: The effect of load capacitor on the crystal Crystal with parallel load capacitor In the case of parallel connection, the reactance part of the crystal becomes inductive. This inductive reactance parallel resonates with crystal’s shunt capacitance (Co) and operates the crystal above its fr. To calibrate this offset, load capacitance (C L) must be specified. Mercury part number, use HC-49/U 10.000 MHz with 20 pF load capacitance as an example, becomes H49-10.000-20P. In the crystal manufacturing processes, manufacturer adjusts the crystal final frequency with a physical load capacitor to simulate the customer’s circuit. Customers can predict a reasonable frequency tolerance from the manufacturer if the load capacitance is specified correctly. The typical load capacitance of modern oscillator circuits ranges from 8 to 32 pF. Typical values include 10, 12, 16, 18, 20, 30 and 32 pF. As seen from figure 4 higher capacitive load makes the crystal frequency go lower. + reactance CL=8 pF CL=32 pF Series resonance fa frequency - reactance fr Fig. 4: Crystal reactance vs. frequency Series crystal does exist but there is no such a thing called “parallel crystal”. A parallel crystal is a series crystal loaded with external capacitances and pulled away from its series resonant frequency (fs). The parallel load resonant frequency fL is given to a good approximation by f L = f S {1 + C 2 (C O 1 + C L ) } ---------------- Equation 2 Equation 3 can be used to predict the effect of frequency change with respect to the change in load capacitances (C L1 and CL2) for a particular crystal ∆f f − f CL = CL 1 f f CL 1 2 = C1 1 1 − 2 (C 0 + C L 1 ) (C 0 + C L 2 ) ---------------- Equation 3 Equation 3 suggests that crystals with smaller load capacitance tend to have higher pulling sensitivity (frequency change per pF load capacitance change). Therefore, small CL value like 8 pF or smaller is not recommended. Equation 3 can also be expressed graphically as MERCURY Technical Note No.: TN- 021 Revision: 0 USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 Date: Jan. 10, 2001 Page 4 of 6 Title: The effect of load capacitor on the crystal ∆f f Zf=Rf +jXf IC Amp. X1 CL (pF) Rf. X2 Ra 100 10 Fig. 5: Crystal reactance vs. frequency Cx1 Pierce Oscillator Cx2 Fig. 6: IC with built-in feedback loop Unlike in the old days one had to build his own crystal oscillators by using vacuum tubes, transistors or even logic gates, recent ASICs if timing signal is required all have integrated amplifier and integrated feedback resistor (Rf) inside the ICs. They are known as “on-chip oscillator”. Some ASICs do not have the integrated Rf. The most common on-chip-oscillator is the positive reactance type oscillator also known as Pierce oscillator as shown in figure 6. It provides economic timing signals for the device because only a few external components required. CX1 and CX2 are two pi-network capacitors in series. The crystal (effectively inductive and to be connected to the X1 and X2 pins of the IC) parallel resonates with Cx1 and Cx2 in the feedback loop and provides approximately 180° phase shift. The amplified signals from the amplifier have 180° out-of-phase with its input signals. Loop gain greater than 1 and 0° (an integer multiple of 360°) phase shift are required to sustain oscillation. Instead of showing X1 and X2 some devices might show OSC1 and OSC 2. One example is Motorola MC68HC05JB4 micro controllers. This device can either take a 6 MHz parallel resonant crystal or a CMOS compatible external clock signal input (to OSC1). Ra is normally not necessary if the drive level (current flows through the crystal) is kept below factory specified value. Depends on the crystal frequency and holder type, the drive level vary from 1 uW (for tuning fork crystal kHz range in 2x6 or 3x8 tubular can), 100 uW (for UM-1 and UM-5 in MHz range),1 mW (for HC-49/U in MHz range) to 2 mW (for HC-51/U in MHz range). Crystal will be degraded or even damaged if it is overdriven for a period of time. The output frequency decreases or becomes unstable when supply voltage increases is an indication of an overdriven crystal. Decrease power supply voltage or increase Ra value will take care of this problem. Also, it is practical in the circuit design stage to have a way to trim the output oscillator frequency. This can be achieved by adding series capacitor to each terminal of the crystal. MERCURY Technical Note USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 No.: TN- 021 Revision: 0 Date: Jan. 10, 2001 Page 5 of 6 Title: The effect of load capacitor on the crystal To improve the oscillator performance Most of the IC data book will give detailed crystal specifications. But because of the variations from layout to layout and applications to applications, using the pre-defined crystals does not guarantee the results. Different layout might have different stray capacitance. The stray capacitance is another part of the load that crystal “sees” in the oscillator circuit. Large stray capacitance reduces loop gain and stability. It can be kept to minimum by placing the crystal as close to the IC as possible, keep the trace short and ground the crystal. Most of the metal can crystals can be ordered with ground lead option. Ceramic packaged crystals such as Mercury MQ series have four contact pads and two of the m are used for grounding purpose. Depends on the power requirement, the conductor width of the PCBs need to be optimized so that unwanted inductance won’t be introduced. To prevent capacitive coupling do not route any digital signal near the X1 and X2 pins. Selection of the capacitor values Like Ra, Cx2 reduces current to the crystal and typically ranges from 5 to 50 pF. Instead of using a voltage regulator in the system, Cx2 value can be increased to reduce the supply voltage effect on the frequency stability. CX1 ranges from 0 to 30 pF assuming the amplifier is an inverter. In some applications Cx2 is a fixed capacitor while CX1 is a variable capacitor so that the oscillator frequency can be fine tuned to the desired frequency mechanically. Higher Cx1 and Cx2 values tend to improve the frequency stability but the increase of the current consumption, start-up time, propagation delay and narrower trimming range all need to be considered. Normally the crystal load capacitance is selected first (mid range such as 20 pF is a good start-up) then Cx2 is chosen and then the Cx1 can be determined experimentally. Normally CX1 and CX2 are equal but not always true. CX1 and CX2 values control the voltages across the crystal. Voltage swings at X1 and X2 need to be controlled at rated values so that additional phase shift won’t be introduced and the gain won’t be attenuated at the amplifier section. If one likes to pick CX1 and CX2 first then figure out the crystal load capacitance, the following equations can be used to predict the CL of the crystal. The combined capacitive reactance of the CX1 and CX2 equals to the inductance reactance of the crystal. The reactance part of the amplifier, Zf (in this case is inductive and Xf=ωL1, ω=2πf), parallel resonates with the series combination of the Cx1 and Cx2 . Therefore, f= 1 , 2π L1Cx where Cx= Cx1∗Cx 2 ---------------- Equation 4 Cx1+ Cx 2 MERCURY Technical Note USA: [email protected] Taiwan: [email protected] Crystal manufacturer sine 1973 No.: TN- 021 Revision: 0 Date: Jan. 10, 2001 Page 6 of 6 Title: The effect of load capacitor on the crystal For more accurate calculation any stray capacitances in parallel need to be considered. Then, CL = Cx1 ∗ Cx 2 + Cstray Cx 1 + Cx 2 ---------------- Equation 5 the oscillation frequency becomes f = 1 2 π L1 C L ---------------- Equation 6 For a fixed frequency, CL can be easily predicted by using equation 4, 5 and 6. Cstray is difficult to measure but 3 pF is a good assumption value. The effective CL value is normally smaller than the calculated CL value due to the amplifier input capacitance. References 1. RCA CMOS integrated circuit s data book SSD-25C, application note ICAN-6086 “Timekeeping Advances Through COS/MOS Technology”. 2. Motorola High Speed CMOS Logic Data Book 3. Eaton, S.S. Micropower Crystal-Controlled Oscillator Design Using RCA COS/MOS Inverters, RCA Application Note ICAN-6539. 4. Robert J. Matthys, Crystal Oscillator Circuits, Wiley-Intersciences, 1983 5. Okano Ohotaro, Quartz Crystal Devices, Hang Kuang, 1998.