Crystal characterization and crystal filter design An overview of techniques and tools Nick Kennedy, WA5BDU April, 2008

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1 rystal characterization and crystal ilter design An overview o techniques and tools Nick Kennedy, WA5BDU April, 2008 Purpose & scope This paper was prepared to parallel a PowerPoint presentation I developed or the Ozarkon QRP convention in Joplin, MO. PowerPoint slides are ine as presentation guides, but typically don t contain suicient detail or use as a stand alone reerence paper. In this paper, I reviewing the techniques or easuring crystal paraeters as ound in a nuber o published articles, typically ha related. I also discussing the instruentation required, which I consider to be o inial cost and coplexity considering the task. The two ajor techniques I call the BW / Q ethod and the shited requency ethod. In the orer, a signal generator and detector are used to deterine the crystal s 3 db bandwidth and its loss resistance is ound by substitution. This is enough inoration to calculate the key paraeters o the crystal odel. With the shited requency ethod, the crystal is installed in an oscillator circuit and the eect o switching a known capacitance in and out o series with the crystal is noted. This allows calculating the otional inductance and capacitance easily. In the second ajor section, I discuss crystal ilter design. The detailed theory and atheatics o ilter design is beyond the scope o this article in general. Rather, I ocus on use o two popular and easily available sotware packages or ilter design. Soe practical aspects o ilter design and construction are covered. The erits o various ilter shapes or response types (Gaussian, hebyshev, etc.) are discussed qualitatively. Introduction The crystal ilter has long been a key coponent in the design o single signal superheterodyne W receivers and other highly selective receivers regardless o ode, as well as in the generation o single sideband signals using the so called ilter type ethod. For soe tie, the design and construction o these ilters has been largely the doain o coercial entities. Only the ost advanced hobbyists having knowledge and equipent out o the reach o ost average hoebrewers attepted it. In the past couple o decades however, a nuber o advanceents have put the design and construction o crystal ilters within the capabilities and pocketbooks o the typical ha builder. These advanceents, which I intend to overview, include the ollowing: Publication o key papers by Hayward, Deaw and others*, which described siple test equipent and procedures or crystal easureent and ilter design. (*In the UK, J.A. Hardcastle and Dave Gordon-Sith published techniques.) Ephasis on ladder type ilters using all crystals on the sae requency was a key actor in reducing cost and coplexity. Availability o inexpensive, highly stable signal generators adjustable to Hz resolution including DDS, PLL and VXO types. Availability o ree sotware capable o designing crystal ilters o various types quickly and easily.

2 Availability o ree sotware to odel and plot the response o proposed ilter designs, allowing repeat analysis and what i testing beore coitting to hardware. Availability o inexpensive crystals on a wide variety o requencies, oten priced at ity cents or less each ro large retailers, and possibly even less ro surplus sources. rystal characterization haracterization just reers to easuring the electrical paraeters o the crystal. But what are the expected paraeters o a waer o a ineral placed between two electrodes? Fortunately, a odel consisting o eleents we know how to deal with (, L, R, ) can be used to approxiate the device s behavior in a circuit to a high degree o accuracy when near the resonant requency o the crystal. 0 X 22 4p 0.07p 0 L Rs The odel o a crystal Equivalent circuit o a crystal L otional inductance otional capacitance Rs equivalent loss resistance o holder capacitance The siplest odel o a crystal is that o a series resonant L- circuit. To allow or the act that crystals have inite Q, we add an equivalent series loss resistance Rs. And inally, consider the act that the waer o crystal is held or contained between two etallic plates or depositions o etal. These parallel plates naturally or a capacitor, which appears in parallel with the L--R odel o the crystal itsel. This adds the ourth eleent to the coplete odel, o. The L and o the series odel are called L and with the subscript ro the act that they are reerred to as the otional paraeters o the crystal. The values in the igure are typical o an 8 MHz H- 49/U crystal. Measureent Methods # Bandwidth & Q Method This ethod uses the act that a series R-L- circuit will have a certain 3 db bandwidth around its resonant peak. (Note that parallel capacitance doesn t aect this easureent ethod and isn t deterined by it.) Two orulas expressing the Q o the R-L- series circuit odel can be used to deterine L and. A easureent o Rs is also required or this ethod. Those expressions or Q are:

3 () Q R BW and, (2) Q X R Where R in () is the resonant requency and BW is the bandwidth at the -3 db points. In (2), X is the reactance o L or (they are equal at resonance) and R is the total series resistance o the circuit. The R value in this equation bears soe ore explanation, as it is usually ore than just the R S o the crystal. In the typical easureent schee, a signal generator o source resistance R g drives the crystal and a detector generally having the sae resistance is connected to the opposite end o the crystal. Thus the coplete circuit has resistance R g + R s + R g, or R s + 2 R g total resistance. The Q easured in this way is called the loaded Q because it includes not only the crystal s loss resistance but also the source and load resistances o the circuit. Now, how are these acts used to easure crystal paraeters? The signal generator, crystal, and detector are connected in series. The point o the peak reading on the detector is ound and noted as the resonant requency. Then the requency is varied below and above that requency to ind the points where the detector shows ½ o peak power (-3 db points). Subtracting the lower ro the higher requency gives the bandwidth. Now we have enough inoration to calculate the loaded Q ro (). Next, R s is easured by adjusting the requency to the peak (series resonant) point and noting the reading. Recall that at this requency, the inductive and capacitive reactances cancel each other so the total ipedance o the crystal is siply R s. The crystal is reoved and a pot inserted in its place. The pot is adjusted to give the sae reading on the detector as just noted. Then the pot s resistance is easured. It is equal to R s. Now we have enough inoration to solve or X in equation (2). R is R s + 2R g as noted earlier, and Q was deterined ro (). Knowing X, we can now calculate L and ro the orulas or inductive and capacitive reactance at the resonant requency. L X/(2*PI*) and /(2*PI**X) OK, but we don t want to work through all these individual calculation steps each tie we easure a crystal, so we coe up with one orula or L and one or using our easured data in one step:

4 (3) 2 π 2 2 R T where and 2 are the upper and lower -3 db requencies and R T is the total resistance o crystal, signal generator and detector. Note that the resonant requency squared can be used in place o the *2 ter in the denoinator with essentially no loss o accuracy. And or L we have, (4) 4π L 2 2 An alternate ethod o easuring or calculating R S is available i the test equipent allows easureent o the loss o the crystal at resonance, in decibels. (Re. 2) This is the dierence in detected power to the load with the crystal at resonance and with a juper installed in place o the crystal. (x) α 20 R S 2R g 0 Where (alpha) is the loss in db and Rg is the source or load resistance, assued to be equal. #2 - Shited Frequency Method The G3UUR Method or easuring L and is considerably sipler in that neither a signal generator nor a detector is required. Only a siple oscillator circuit and requency counter are used. With this ethod, the crystal is installed in a olpitts oscillator circuit. The circuit allows grounding the low end o the crystal directly or through a sall capacitor s (uch saller than the olpitts divider capacitors). Frequency easureents are ade with the capacitor in circuit and out o circuit and the delta between the is calculated. and L are then calculated using the ollowing: and (5) (6) 2( s + o ) (2π ) L 2

5 This ethod is siple and ast, but it does not provide a value or R S. Note that soe published versions o equation (5) oit o. This is probably unintentional, since its eect is signiicant. The equations above neglect the eect o the olpitts voltage divider capacitors, since they are large with respect to s. But in the interest o axiu accuracy, I derived this version o equation (5) which includes those capacitors: (7) ( )( 2) Where and 2 are calculated in ters o olpitts capacitors c and c2 and s as ollows: (7a) S O (7b) And and 2 are the requencies with s in and out o the circuit, respectively. L is then calculated ro equation (6). O #2a hris Trask circuit & ethod A variation on the shited requency ethod is the hris Trask (N7ZWY) ethod and circuit that he published to the web in February, His circuit is designed to have the crystal oscillate on its actual series resonant requency, eliinating approxiations associated with the G3UUR circuit. It is soewhat ore coplex in that it incorporates AG to keep the oscillator waveor sinusoidal. It also provides or an RF voltage drop easureent directly across the crystal or use in calculating R S. Required test equipent or crystal easureents Bandwidth / Q easureent technique: ) A signal generator, stable and accurate to Hz with known source resistance. (Source resistance can be assured with resistive pads.) The output should also be a clean sine wave, ree o haronics. Incorporate low pass iltering i necessary. a) A VXO, such as K8IQY's PVXO circuit b) A DDS synthesizer, such as an NJQRP unit c) A PLL/VO oscillator, such at the MultiPig VFO

6 2) A requency counter, unless a DDS is used 3) A detector. This is a eans o easuring relative RF voltage or power into a known load resistance, usually 50 ohs. Absolute accuracy is not required because a 3 db pad is used to deterine the -3 db points. a) A siple diode type detector and DMM is suicient i drive level is high enough b) For lower levels, an apliied & copensated type diode detector, such as the NORTEX Accuprobe ight be used c) A log RF power eter such as kitted by Kanga is suitable although ore sophisticated than needed or this application d) An oscilloscope is another option or the detector 4) A switchable 3 db resistive attenuator. Easily built with three resistors and a toggle switch. 5) A sall value non-inductive potentioeter and an oheter G3UUR Method (easures L and but not Rs) ) A siple (two transistor) crystal oscillator circuit with crystal socket 2) A requency counter accurate to Hz hris Trask (N7ZWY) Method ) Measureent circuit published by N7ZWY 2) Frequency counter accurate to Hz 3) Oscilloscope or RF volteter (needed or Rs easureent only) With any o the ethods used, easureent o o is perored using a capacitance eter accurate to 0.pF such as the AADE or Elsie circuits. o ay also be estiated to good accuracy with no easureent needed. Quotes, acts, tips, opinions & one-liners about crystals & crystal ilters o (holder capacitance) is usually approxiated by o 220, which is derived ro the physics o an AT cut crystal. In practice add 0.5 to pf to this value. () (2) Always ground the crystal case. (3) (Note that soe authors state that they do not ground the case or ear o daage caused by soldering.) I the crystal case is grounded, reduce the easured o by hal the capacitance easured ro both pins shorted together to the case. (3) hebychev ilters tear up the tied pulses o RTTY, AMTOR, or lover signals. Two good choices or data odes are Gaussian-6-dB and Gaussian-to-2 db designs.

7 Filter bandwidth has been ound to be inversely proportional to the square root o the coupling capacitance. (6) Wider ilters operate at higher ipedances and have saller coupling capacitors. (7) Miniature, wire-ended crystals (e.g., H49/U) require a higher circuit ipedance than H-6/U types. (6) A hebyshev with 0. db o ripple is the ost coonly used response type or SSB HF ilters. (9) The recoended requency range or an SSB crystal ilter is between 6 and 2 MHz. (9) There is no physical dierence between a parallel and a series type crystal. hoose crystals with a axiu requency spread o about 0% o your ilter bandwidth Fro (5), the dierence in the series and parallel resonant requency o a crystal can be approxiately airly closely with this orula: 2 o Where is the noinal requency o the crystal, is the otional capacitance and o is the holder capacitance. Fro (6) (AADE quoting Hayward), the noralized Q o the ilter ust be greater than twice the nuber o crystals in the ilter, or 2 * # o crystals < Qu * BW / where Qu is the unloaded Q o the crystals, BW is ilter bandwidth and is the crystal requency Reerences () Reineents in rystal ladder Filter Design, Wes Hayward, W7ZOI QEX June 995 (2) An Oscillator Schee or Quartz rystal haracterization, Wes Hayward, ro his web page (3) Why rystal Filters? Bill arver, W7AAZ notes or FDIM presentation (4) Designing and Building Siple rystal Filters, Wes Hayward, W7ZOI QST 7/87 * (5) A Tester or rystal F, Q and R, Doug DeMaw, WFB, QST /90 * (6) Ladder rystal Filter Design, J.A. Hardcastle, G3JIR QST/80 * (7) High-Perorance rystal Filter Design, Bill arver, ounications Quarterly, Winter 93 * (8) Soe Experients with High-Frequency Ladder rystal Filters, J.A. Hardcastle, G3JIR QST 2/78

8 (9) Designing and Building High-Perorance rystal Ladder Filters, Jacob Makhinson, N6NWP QEX /95 (0) rystal Motional Paraeters A oparison o Measureent Approaches, Jack Sith, K8ZOA 6/06 ro the web - () A Practical Test Set or oprehensive rystal Testing, hris Trask, N7ZWY ro his web site (2) "Designing the Z90's Gaussian rystal Filter", Jack Sith, K8ZOA, QEX May/Jun 2007 (3) Sipliied Tools and Methods or Measuring rystals, Ji Kortge, K8IQY, AQRP Hoebrewer #7, Spring 2006, (also issue #6, Suer 2005) (4) Build a Precision Variable rystal Oscillator, Ji Kortge, K8IQY, AQRP Hoebrewer #6, Suer 2005 (5) Quartz rystal Resonators and Oscillators, John R. Vig, U.S. Ary ounications- Electronics oand, AD-A (6) Filter Design progra Help text, AADE (Neil Hecht)