APPLICATION NOTE
Tone Generation - An Application of the MX105A
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
This Application Note describes how to configure an MX105A as a tone generator. It may be helpful to refer
to the current MX105A data sheet before reading this document. The MX105A was primarily designed as a
tone detector with user configurable center frequency, detection band width and response/de-response time
(refer to the MX105A data sheet for this use). However, it can also be configured as a low distortion
sinusoidal tone generator with minimal filtering. Figure 1 depicts a recommended circuit configuration for tone
generation. Figure 2 details the circuit of Figure 1 by showing a block diagram of the active circuits in the
MX105A used for tone generation.
MX105A
C1A
C1B
R3
R2
C5A
C5B
R5B
R5A R1
RL
2
3
4
5
6
7
8
115
14
13
12
11
10
9
16
TONE OUT
VDD
VSS
C6
Figure 1. Simple Tone Generation Circuit using MX105A.
TONE GENERATION An Application of the MX105A 2 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
1. Circuit Description for Tone Generation.
An RC oscillator (pins 13-15) generates an internal clock at six times the center frequency. This clock is
internally decoded to sequentially enable four analog switches configured between pins 3 and 5 (SW3A),
pins 3 and 6 (SW3B), pins 4 and 7 (SW2A), and pins 4 and 8 (SW2B). The control signals for these switches
are shown in Figure 3. The switch connections to R2 and R3 form a simple Digital to Analog converter to
produce a three level approximation of a sine wave ( 1 1 0 -1 -1 0 . . .) as shown in Figure 3. This waveform
is well suited for tone generation as described below. Finally, a simple low pass filter formed with the on chip
buffer amplifier smoothes the three level sine wave to produce a low distortion sine wave.
Note: A large value DC blocking capacitor should be used at pin 2 if pins 6 and 7 are driven for tone level
control or amplitude modulation as shown in Figure 2.
4
V or Optionally drive signal here for
amplitude control or AM modulation
DD
15 14 13 4 3 1 2
200kΩ1kΩ
SW3A
SW3B
SW2A
SW2B
V
SS
6x TONE
FREQUENCY
OSCILLATOR
DIGITAL TO ANALOG
CONVERTER LO W PASS FILTER
TONE OUT
RC OSCILLAT OR
SWITCH
CONTROL
LOGIC
V/2
DD
1
8765
R1 C1A C1B R2 R3
R5A R5B
C5B
C5
Optional DC
blocking cap
C5A
Figure 2. Block Diagram of Tone Generation Circuit.
TONE GENERATION An Application of the MX105A 3 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
Three Level
Sine Wave
SW2A
SW3A
SW2B
SW3B
Figure 3. Internal Switch Control Signals and Resulting Three Level Waveform.
1.1 Fourier Series Analysis of the Three Level Waveform.
The periodic three level approximation of a sine wave can be represented by the following formula:
f(t)
Afort
T
6
0T
6tT
3
Afor
T
3tT
2
where T is the period
Fourier Series Expansion of f(t) yields the following coefficient formulas after some calculus:
a2
TfTd
2A
T
n
tntt
A
nnn
( ) cos
sin cos
,,,, ,, ,,,, ,, ,
2
21
312 1
3
31
1000 1
501
7000 1
11 01
13
0
for positive integer n
b2
TfTd
T
n
tntt
( ) sin 20
0
for positive integer n
These coefficients result in the following fourier series representation:
ft t t t t t
( ) cos cos cos cos cos
2A TTT T T
321
5521
7721
11 1121
13 13 2
This function is plotted in the time domain in Figure 4 and in the frequency domain in Figure 5. It is clear from
the frequency domain plot that the first harmonic spur above the fundamental, the fifth, is already about 14 dB
down. Thus the required filtering to pass the fundamental while suppressing the harmonics is simplified
compared to a square wave.
TONE GENERATION An Application of the MX105A 4 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
0
A
-A
0 1/6 1/3 1/2 2/3 5/6 1-1/6-1/3-1/2-2/3-5/6-1 time (normalized to period T)
Fourier Series Expansion of D/A Output to 31 terms
Figure 4. Time Domain Plot
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
dB (w.r.t. fundamental)
frequency (normalized to tone frequency)
Harmonic Content of D/A Output
Figure 5. Frequency Domain Plot
TONE GENERATION An Application of the MX105A 5 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
1.2 Analysis of the Low Pass Smoothing Filter
A simple second order filter can provide 12 dB per octave roll-off in the filter’s stop band. Thus we can expect
as much as 27 dB (i.e.
27 12 5
2
dB
log ) attenuation of the fifth harmonic and above with such a filter.
This should produce a sine wave with distortion of about 1% (i.e. harmonics more than 40 dB down). More
complex filtering can be used if lower distortion is required.
A simple second order low pass filter (formed with R5A, R5B, C5A, C5B, and the internal buffer amplifier
between pins 1 and 2) suppresses the harmonics of the three level waveform to produce a low distortion
(<1%) sine wave at pin 2. The transfer function of this low pass filter including effects of the input impedance
of the MX105A buffer amplifier is:
H( )
Ri
R5A R5B Ri R5A R5B Ri
C5A C5B R5A R5B Ri
R5A R5B Ri
C5A C5B R5A R5B Ri 1
C5A R5A 1
C5A R5B 1
C5B Ri
2
jj
choosing to let R = R5A = R5B and C5A = 2 C5B and substituting C = C5B results in
H( )
Ri
2R Ri 2R Ri
2C R Ri
2R Ri
CRRi 1
CR 1
CRi
22
22 2
jj
2
From this expression the equation for the pole frequency is: (
f
p
is plotted in Figure 6 to help in component
choices).
pp
f
2222
2R Ri
CRRi
2R Ri
CRRi
22
22
The equation for the Pass Band DC Gain is: (plotted in Figure 7 to help in component choices).
DCGain Ri
2R Ri
100
1000
10000
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Approximate Cutoff Frequency (Hz)
R (kΩ)
100pF
150pF
220pF
330pF
470pF
680pF
1000pF
1500pF
2200pF
3300pF
4700pF
6800pF
0.01uF
0.015uF
0.022uF
Figure 6. Approximate Cutoff Frequency Design Chart
TONE GENERATION An Application of the MX105A 6 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Approximate Pass Band Gain (dB)
R (kΩ)
Figure 7. Approximate Filter Gain vs. R
Note that this filter provides attenuation in the pass band due to the input impedance of the buffer amplifier.
The filtered tone level will be:
Approximate ToneLevel (in V ) ARi
2R Ri
dB Gain
20
p-p 1.1 A 10
23
where A is VDD or optionally the level driven into pins 6 and 7 and dB Gain is read
from Figure 7.
TONE GENERATION An Application of the MX105A 7 Application Note
©1998 MX-COM Inc. www.mxcom.com Tel: 800 638-5577 336 744-5050 Fax: 336 744-5054 Doc. #20830069.002
4800 Bethania Station Road, W inston-Salem, NC 27105-1201 USA All trademarks and service marks are held by their respective companies.
2. A Worked Design Example - 1700 Hz Tone Generator
The tone frequency is set according to the standard formula in the MX105A data sheet:
F6 R1 C1A ln(2)
0
1 with C1A = C1B
To generate a 1700 Hz tone while choosing C1A = C1B = 680pF
R1 6F C1Aln(2) 6ln(2)
11
1800 680 10
012 208 k
Choosing R1 = 150k in series with a 100k potentiometer will allow frequency tuning if required.
Referring to Figure 6 to pick R after choosing C = 680pF for the low pass filter results in:
R = R5A = R5B = 130k
C = C5B = 680pF and C5A = 2 x C5B 1500pF
Calculating the approximate pole frequency to check design choices:
f
2R Ri
C5A C5B R Ri Hz
2
21838
(seems reasonable)
Calculating the approximate tone level for VDD = 5V results in:
ToneLevel 1. A
-7
20 Vpp mVRMS
1 10 246 870.
If tone amplidude control is required, drive a DC level (A) into pins 6 and 7 and use DC
blocking capacitor C5 as shown in Figure 2.
Finally, choose R3 and R2 sufficiently low compared to R so as not to significantly affect the filter's frequency
response and gain. For example, choose R3 = R2 = 10k
The filter graphs and design example are based on the typical buffer input impedance of 200k This
parameter varies from device to device and with supply voltage. The input impedance is approximately
proportional to 4
V1
DD and may vary from 160k to 360kat VDD = 5V. These figures are given to help the
designer analyze for device variation; they are not guaranteed specifications! Refer to the MX105A for all
specifications. A smoothing filter built with an external amplifier may eliminate these issues.
Note: In this design example the filter cut off may vary from 1720 Hz to 2120 Hz and the filter gain may vary
from -8.2 dB to -4.6 dB due to the buffer ‘s input impedance. Even with these variations the second order
filter should provide good attenuation of the 1700 Hz tone’s 5th harmonic and above.
