### AN9815: Crystal Filter Yields Pure Sine Waves

```Crystal Filter Yields Pure Sine Waves
Application Note
June 1998
Introduction
2
V
2
T
3.3
R ≥ ---------------- = ----------- K ≈ 2.2K
P MAX
5
Electronic applications such as distortion and communications measurements require pure (distortionless) sine waves
as input test signals. Distortion contained in test signals
causes two problems. First, the test signal distortion content
must be calibrated so it can be subtracted out of the measurement. Second, processing a distorted test signal usually
creates unique harmonics which cause false readings
because they can’t be calibrated out.
R and C1 form a low pass filter which kills the high frequency
response and filters out noise. The -3dB point for R, C1
should be set at one tenth the crystal frequency or 5MHz/10
= 500KHz. C1 is calculated from Equation 2.
1
1
C 1 = -------------- = --------------------------------------------------- = 144pF ≈ 150pF
2πfR 2π ( 5EE5 )(2.2EE3)
TEST
SIGNAL
R
2.2k
C1
150pF
(EQ. 2)
Load capacitance changes tend to pull the crystal, and C3
should be large so changes are a small percentage of C3 .
C3 is usually selected as approximately 3 times C1 . Let C3 =
510pF. The series combination of C1 , C2 , and C3 should
equal CL = 32pF specified by the crystal vendor.
(EQ. 3)
1
1
1
1
------- = ------- - ------- - ------C2 CL C1 C3
The crystal is surrounded by a π network which preserves
The crystal must be parallel resonant to function with the π
capacitance, CL, and the maximum input power, PMAX .
The series resistor, R, limits the crystal power, and
although it is an optimistic approximation, Equation 1 can
be used to select R.
5MHz
CRYSTAL
(EQ. 1)
For V T = 3.3V and P MAX = 5mW
Signal sources which approach distortionless operation are
available, but they are expensive, bulky, hard to use, and
overkill for simple applications. The crystal filter described
here utilizes any inexpensive sine wave generator to supply
the test signal, and it filters the distortion out of the test signals prior to the measurement. This crystal filter is inexpensive, simple to design, and it reduces 2nd harmonic
distortion by 70dB. Configured as shown in the schematic
with the HFA1112 buffer, it can drive back terminated 50Ω
loads while reducing distortion 63dB. Furthermore, driving
the crystal filter with a square wave test signal only
increases the 2nd harmonic content by a fraction of a dB.
C2
43pF
AN9815
C2 calculates 44.2pF, so it was selected as 43pF. With the
component values shown in the schematic, the -6dB bandwidth is 144Hz, and this equates to a crystal Q exceeding
45,000. The crystal filter must be constructed using a ground
plane and other similar high frequency techniques. Reducing
the value of C2 by 10pF, and adding a 20pF variable capacitor in parallel with C2 yields a 0.1% adjustment of the filter’s
center frequency. This adjustment range can compensate for
normal manufacturing tolerances.
+5V
HFA1112 7
3 + 6
C3
510pF
2 4
RT
FILTERED TEST
SIGNAL
-5V
FIGURE 1. CRYSTAL FILTER
1
Application Note 9815
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2
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