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Barker Code-Locked Loop Synchronous Demodulator
A simple, low component count phase locked loop that locks onto and detects the amplitude of an incoming baseband 7 bit Barker code
using a switched resistor demodulator that is driven directly by a microcontroller's output pins.

• Balanced modulators using resistors and a microcontroller's output pins.
• Locking into oncoming Pseudo-noise (PN) stream.
• Microcontroller modulates its own crystal oscillator frequenc inside a Phase-Locked Loop (PLL). 
• Extending the output range of a bipolar op-amp to opearte near ground.

Photo 1. The only semiconductors in the circuit are the microcontroller
and a quad opamp. This picture was taken
before the offset adjustment
for the signal level measurement circuit was installed.
Some surface
mount components are on
the other side of the board.
Click on the image above for a larger version.

Download the AVR Studio assembly source for the ATtiny12 7 bit Barker beacon: Brkshf061015B.asm
Download the AVR Studio assembly source for the ATtiny2313 demodulator / 7 bit Barker source: bark3p061015A.asm
Download the AVR Studio assembly source for the ATtiny2313 181.818 kHz Barker code transmitter: rf7bark061015B.asm

Find updates at www.projects.cappels.org

Related web pages:   
Digital Lock-in Milliohmmeter  http://cappels.org/dproj/dlmom/dlmom.html
Experimental 1 kHz Synchronous Demodulator  http://cappels.org/dproj/syncdet/syncdet.html                      

Figure 1. This simple circuit includes three synchronous demodulators and two
integrators that process the demodulation signal. The modulation is achieved by switching
the microncroller's I/O pins between high impedance and current sinking states, so no additional
analog switches or multipliers are needed. The first op-amp stage (pins 8,9, and 10) is used
to provide a uniformly low output impedance to the demodulators. It can be converted to a gain
stage or a filter, provided there is sufficient loop gain to maintain a sufficiently low output impedance.


After a successful synchronous demodulator project, as described in Digital Lock-in Milliohmmeter and Experimental 1 kHz Synchronous Demodulator, I looked for a way to improve upon on the basic synchronous demodulator that I used in those projects. I was looking for a way to reduce the component count, eliminating the transmission gates if possible. I also wanted the demodulator to be able to lock to signal from a remote source, all the while maintaining the benefits of noise rejection and processing gain that one would expect from a synchronous demodulator,  because such a circuit might lead to a simple but robust modulation and demodulation scheme for RF communications. 

The circuit in figure 1 is that of a synchronous demodulator that meets these requirements, and additionally, it operates from a single positive power supply. The circuit will be described in detail later in this page. The ATtiny2313 microcontroller is  used as a voltage controlled crystal oscillator and Barker code generator, and could be replaced with small scale logic devices. The code generation is initiated by interrupts from the microcontroller's internal 8 bit timer, and there is plenty of time available for control and computational tasks that could used to modulate the Barker code stream with data or to decode an incoming stream. The ATtiny2313 has three Barker code outputs, shifted one half of a chip in period (the time period allotted to one bit in the Barker code) from one-aonther, that appear to the external circuitry as though they are open drain outputs,  it has three regular CMOS outputs that are similarly time shifted with respect to one another, and it has a sync output that occurs one time with each repetition of the Barker code. The sync signal is to facilitate testing of the circuit.

This implementation, using a 7 bit Barker code with a 148 microsecond chip rate, was intended as a means of proving a concept. The low chip rate was selected because it is easy to deal with using the inexpensive equipment available to me.  A longer Barker code and a faster chip rate would increase performance, and merely scaling the design will provide those improvements.

Figure 2. The circuit of an infrared beacon, which transmits a continuous
stream of the 7 bit Barker code. The Barker code gates a 50 milliamp
constant current source made of the two 2N4401 transistors.

As a test signal source, I programmed an ATtiny12 microcontroller with code similar to the ATtiny2313 and uses its code output pin to drive a gated constant current source, which in turn drives an infrared LED with 50 milliamps. The LED emitted light in accordance with the Barker code sequence sent from the chip.
As with the ATtiny2313, this function could be easily replaced with discrete logic. In addition to the code output, the ATtiny12 also has a sync output that occurs one time with each repetition of the Barker code.

In an experiment to visually illustrate operation of the demodulator, I connected a photo diode between the signal input and "ground" on the demodulator circuit in Figure 1 and used the 7 bit Barker code beacon shown in Figure 2. There was no electrical connection between the beacon and the demodulator, except that their power supplies were plugged into the same electrical outlet. During some experiments, the beacon was battery operated, and I did not notice any difference in performance between those experiments in which the beacon was battery operated and those experiments in which the beacon was powered from a power supply.

Before testing, the free run frequency of the demodulator had to be set. Channel one of a Tektronix TDS-2002 oscilloscope was connected to the  punctual Barker code output pin on the ATtiny2313 (ATtiny2313 pin 18), and scoope was sync'd to the sync output of the ATtiny2313 (ATtiny2313 pin 16). Channel two of the scope was connected to the Barker output of the ATtiny12 on the beacon assembly (ATtiny12 pin 7) and the infrared LED on the beacon was covered so demodulator would not detect the beacon's signal. While simultaneously viewing the prompt Barker code generated on the demodulator and the Barker code generated by the beacon, the free run frequency of the demodulator was adjusted so that rate of local prompt Barker code generation was fraction of a word per second slower than that of the beacon.

Channel two of a Tektronix TDS-2002 oscilloscope was then moved to the  output of the voltage follower stage in the demodulator (LM324 pin 8) and the IR LED on the beacon was uncovered. letting some of the light from the LED fall on the photo diode connected to the demodulator. Photo 1 and Photo 2 show what the signals looked like.

Photo 2. This is a screen shot while the scope (Tektronix TDS-2002)is in the sampling mode. The blue trace shows the incoming signal from a photo diode, with the noise provided by fluorescent lights and a dangling 1 meter clip lead. The yellow trace is the prompt Barker code generated by the ATtiny2313 on the demodulator. The scope was synchronized to the sync output on the ATtiny2313.

Even though the singal-to-noise ratio was rather poor, the demodulator managed to lock to the incoming signal and so provided sync for the scope, so when I switched the scope to Averaging mode, in which the waveform was averaged over 128 cycles, the received waveform was displayed clearly.

Photo 3. This is a screen shot while the scope (Tektronix TDS-2002) was in the averaging mode, showing the incoming signal from a photo diode, with most of the noise removed by integration. The effect is similar to what happens in the circuit -the demodulated signal is integrated and the 50 Hz and other noise signals are average to a low value, leaving the signal.

The averaging of the waveform samples by the oscilloscope is analogous to the function of the demodulator. The average value of random noise is zero. Nearly every signal that is not the expected Barker code appeared as noise to the integrators following the demodulator stages, and since the output of the integrator is the average of input signals over a period of time, the noise was averaged to a very low level.


To appreciate the basics of lock-in amplifiers, please read the article,  Digital Lock-in Milliohmmeter. The article explains and illustrates the concepts in some detail. The Lock-in Milliohmmeter described in the article uses a 1 kHz square wave which is generated by the microcontroller, converted to a current waveform, and then measured through the process of synchronous demodulation. Another article about the same synchronous demodulator,
Experimental 1 kHz Synchronous Demodulator, examines the sensitivity of the demodulator and its ability to measure very small signals in spite of the circuit relying on a quad op-amp that is not known for its low noise performance or exceptional DC stability.

The main problem with using a simple square wave for low level measurements is that they are susceptible to noise, especially at the signal frequency and its odd harmonics. One solution to this susceptibility is to transmit and demodulate with a signal that is made of many different frequencies, one that effectively looks like random noise, but isn't really random. This signal is referred to as pseudo noise, or PN, in many signal processing articles. Figure 3 and Figure 4 show the 7 bit pseudo random sequence used in this series of experiments. This 7 bit sequence is the 7 bit Barker code. All versions of a particular Barker codes that are inverted and/or shifted in time are the same Barker code.

Figure 3. The 7 bit Barker code.
In these experiments, the 7 bit
code is repeated 970 times per second.


Figure 4. Two repetitions of the 7 bit Barker code. In
actual application, a continuous stream is generated.

A barker code was used because they are ideally suited for determining correlation of signals. Barker codes up to 13 bits in length have been found. It is not known, but it is widely held that longer Barker codes do not exist, meaning that there are only seven Barker codes (of length 2, 3, 4, 5, 7, 11, and 13 bits). Pseudo noise codes of greater lengths can be used in this application, and indeed, the longer the PN code, the less susceptible the system will be to interference. I used the 7 but Barker code because it is the longest Barker code that fits inside the AVR microcontroller's 8 bit registers, and 7 bits is sufficient to demonstrate the behavior of the system.

Demodulation process

Figure 5. Block diagram of a synchronous demodulator.

The result of averaging or integrating of AC coupled random noise over a long period of time be nearly zero.

To start with, a 7 bit Barker pseudorandom noise pattern is transmitted.

The synchronous demodulator uses the same pseudorandom noise pattern to demodulate, or detect the incoming signal.

When a pseudonoise signal is used to demodulate the incoming signal and its accompanying noise, the incoming PN signal will be rectified -that is, it is converted to a DC value, while and DC offset, the accompanying noise and other signals will be converted to a noise pattern. The DC modulated by the PN sequence will be the PN sequence, with its amplitude corresponding to the level of the DC voltage into the demodulator, and the noise into the demodulator will become sidebands to the frequency components of the PN sequence.

The output of the demodulator drives an integrator, which averages the signal over time.

As a result, the DC and noise accompanying the incoming Barker code (PN sequence) is converted to noise, which is averaged to near zero, while the incoming Barker Code is converted to a DC level which can be measured.

It should be noted that the demodulator acts by modulating the incoming signal by the PN sequence with a four quadrant multiplier.


The process of demodulation is accomplished by multiplying, or modulating, the incoming signal by a locally generated signal that is the same PN sequence at the same frequency and in the same phase as the incoming signal. The problem of synchronization is discussed in the next section.

The incoming signal is demodulated by three switched resistor modulators.  This switched resistor modulator accomplishes full four quadrant multiplication by switching a node of a resistor network to ground according to the locally generated PN sequence.  An advantage of this circuit over some candidate circuits is that the modulation action can be accomplished with the switching action of a microcontroller's output pin or an open collector, or open drain digital output so that an analog multiplier is not required.

The definition of four quadrant multiplication is shown in table 1. In this table, the input signal is analog, and the local PN code is bipolar. The Local PN code, which is used to demodulate the input signal can only have the values of 0 and 1 because the switching is performed by a microcontroller's digital output pin.

Table 1. Results of four quadrant multiplication.

The function of the modulator can be seen as switching between the input signal (+) and an inverted input signal (-). Figure 6 and Figure 7 illustrate the modulator in action. In the illustrations below, S1 and S2 represent CMOS microcontroller output pins that are switched between high impedance and current sinking states.

Figure 6. Switched resistor modulator in the
"closed" position, where the modulating signal
is considered to have a value of -1. The output
signal appears on the output, inverted.

Figure 7. Switched resistor modulator in the
"open" position, where the modulating signal
is considered to have a value of +1. The output
signal appears on the output, not inverted.

When S1 is closed (Figure 6) , only current from the univerted signal current enters the op-amp's summing node through R12, resulting in an inverted waveform at the output of the op-amp. When S1 is open (Figure 7) current from the uninverted signal and twice as much current from the inverted signal enter the summing node of the op-amp, resulting in an uninverted signal on the output.

In the actual circuit, there is a large capacitor across the op-amp's feedback resistor, so there are no pulses at the output of the op-amp. Instead, there is a DC voltage, which is proportional to the amplitude of the incoming signal.

in practice,  when using these demodulators with a single power supply, the switching of the resistor networks to ground causes an offset on the integrators' outputs. The offset can be adjusted out by adding an offset signal to the summing node.

There is also an imbalance in the signals that results in some of the modulating signal feeding through. The imbalance is the result of a slight difference in the inverting and non-inverting gain of the circuit. This imbalance can be trimmed out by varying one of the input resistances, most easily by making R1 adjustable.

Phase Lock

The phaselocking method is based on the method described in an article by James A. Vincent, G1PVZ, Spread Spectrum: Voice Over Spread Spectrum Radio. In Mr. Vincen'ts article, a PN code is generated and it is delayed to provide three phases. One, the "early" phase is first, followed by a "punctual" phase, which is then followed by the "late" phase. The three phases are separated by 1/2 of a chip, or bit time.

Since I am only dealing with baseband signals, I was able to eliminate the RF and IF circuitry and the separate integrators for early and late codes that Mr. Vincent used, and combine the demodulator's outputs at the summing node of the integrator. The principle of operation is the same. The local Barker code generator is made to run just a little slower than that of the incoming signal. This causes the signals to slide past one-another in phase. When the signals line up, the output of the integrator, which controls the oscillator frequency, changes to provide negative feedback to the phase/frequency loop and locks the local punctual Barker code generator in synchronization with that of the incoming signal. You can see this happen in the video clip (Clip 1) below.

Clip 1. Click on the image above to
see and MPG video of the code locked
loop locking up. The loop's response
is clearly underdamped.

The free run frequency of the local Barker code generator is adjusted by adjusting the offset pot on the phase lock integrator (op-amp pins 5,6, and 7). The ratio of the demodulator resistor values to the op-amp feedback resistor value, in conjunction with the VCXO's sensitivity (the ATtiny2313 in conjunction with the ceramic resonator and the varactor) set the DC loop gain of the code-locked loop, and along with the difference in frequencies between the incoming PN rate and the local PN code rate, ultimately determine the maximum static phase error and the maximum hold frequency range. Making the feedback resistor larger would increase the loop gain and that would reduce the maximum static phase error and increase the maximum hold frequency range.

The AC feedback element in the schematic is simply a capacitor. Generally larger capacitors mean lower susceptibility to noise, and a smaller frequency pull-in range. I tried a more complicated lead-lag network (a 100k resistor shunted by a small capacitor in series with the 0.47 uf integrating capacitor) and confirmed that the loop can be made to pull in over a wider range of frequencies, and pull in a lot faster with a lot less overshoot and ringing. I put the original 0.47 uf capacitor back in place to continue the experiments.

The match between frequencies is very critical, and I had to hand select pairs of crystals and ceramic resonators to work in the signal sources and demodulators. I found that I could pull ceramic resonators over a much larger frequency range than I could pull crystals, and settled on ceramic resonators for the experiments. The problem with using pairs of crystals was that the match was very critical because of the small pull range, and thus selection of pairs was very tedious.

It should be noted that the code locked loop only locks up properly with an incoming phase of the same phase as the punctual output signal from the chip. As coded, that is with four logic lows and three logic highs per 7 bit Barker code. The code-locked loop will not lock to signals of such high amplitude that they drive the analog buffer and/or inverter into saturation.

Amplitude Measurement

A third demodulator is connected to a second integrator. This demodulator is driven by the punctual code.  The integrator has an offset adjustment that allows compensation for the offset created by switching the resistor network in the demodulator to ground, and it is also used to position the integrator's output at an arbitrary level with no input signal.

Figure 8. Output voltage of the punctual integrator
as a function of input signal in millivolts peak-to-peak.

Figure 8 and Table 2 show the input to output transfer function. As expected, the transfer function is fairly lineary as long as the incoming signal remains within the linear range of the buffer and inverting amplifier.

The input signal is AC coupled to a 90 millivolt reference. The value 90 millivolts was selected to minimize the amplitude of the offsets created by switching the resistor networks to ground. The outputs of the LM324 amplifiers can swing as low as about 30 millivolts DC, thanks to some current sinking help provided by the 300 ohm resistors from the op-amp outputs to ground. The inversion in the slope of the transfer function is the result of clipping of the negative peak on the input buffer stage. The input buffer stage is used to provide a stable low impedance with which to drive the switched resistor demodulators.

Values  in millivolts            
input      output    error compared to fit       
0.0        16        16.3       
1.1        21         0.0       
1.5        31         2.5       
2.8        58         2.8       
3.8        76         1.6        m = 19.5662
6.4       130         5.2       
8.6       176         7.1       
12.5      253         8.0       
17.6      345         0.5       
23.8      463        -2.4       
30.7      601         0.5       
37.4      732         0.0       
66.4     1183         -2.9       
68.0     1211         -3.4       
70.6     1261          0.0       
110.0    1971          6.3        m =17.86
144.0    2401       -171.0       
178.0    2041      -1138.4       
204.0    1771      -1872.8

Table 2.  Punctual integrator output voltage as a function
of input code in millivolts peak-to-peak.

RF Transmission and detection/measurement example

Just as a physical proof of concept, I whipped up firmware for 181.8 Khz transmitter that is modulated by the 7 bit Barker code, programmed an ATtiny2313 with the firmware, and connected my 1 square meter loop antenna to it through a 1k resistor to limit current. Then I built a simple TRF (tuned radio frequency) receiver, using a 5.5 cm long ferrite rod antenna.

Within 1 meter of the loop antenna, the receiver was able to lock onto the transmitted Barker code.

Figure 9. Attachment of the 1 square meter
loop to the ATtiny2313 transmitter chip.

Photo 4.  This antenna was made with a frame
of 1/2" PVC pipe and running a length of 0.5 mm
square stranded copper wire (1 conductor of zip
cord) through it. 90 Degree elbows are at three
corners and a "T" is at the fourth corner
(lower right-hand corner in this photograph),
providing an exit for the 50 cm wire leads.
DC resistance is approximately 0.2 Ohms, and
the inductance is 6.2 microhenries.

Figure 10. A very simple TRF receiver
using a 5.5 cm long ferrite antenna
tuned to 181.8 kHz.

All this proved is that the PN code can be transmitted as sidebands on an on-off keyed carrier, and that this can be detected, demodulated, and locked to. The signal level output (op-amp pin 1) indicated signal strength.


Ideas for applications

The 7 bit Barker code repetition rate for this implementation is only 970 times per second. I used this rate because it is slow enough to be very easy to work with. I suspect that with some care, a microcontroller could generate the code at several hundred thousands of repetitions per second, and with logic, much, much higher rates could be achieved. With higher chip rates, which are 7 times the code repetition rate, comes the ability to use a higher corner frequencies on the integrators, and thus the ability to send higher speed data. In addition to measuring the amplitude of the incoming signal, I have, with minor experiments, confirmed that data can be encoded on the code stream and detected by making small shifts in the chip rate. The only drawback for pure base band use is that polarity must be maintained.

Here are some ideas:

• Communications by monitoring the signal amplitude pin or chip rate as a function of time, for
    - RF
    - Optical
    - Through-the-earth or cave radio
    - Acoustic/ultrasonic/infrasonic

• Monitoring of signal level, especially in the presence of noise for
    - Earth and liquid resistance
    - Strain gauges
    - RF
    - Densitometry
    -Acoustic ranging and volume measurement

• Robust HF, LF, or VLF Spread Spectrum RF communications by modulating onto a carrier.

And a note of caution

In addition to my regular disclaimer, which is at the bottom of this page, I would like to point out especially for this project, that many patents have been issued and certainly many applications have been filed on this and related fields. The chances are very high that many aspects of the concepts and implementations discussed on this web page are already covered in patents. You are responsible, not I, for assuring that any use you might contemplate for the techniques discussed or shown here do not infringe on the rights of others.

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Contents ©2006, 2007 Richard Cappels All Rights Reserved. Find updates at www.projects.cappels.org

First posted in October, 2006. Corrections April, 2007. Editorial enhancements October, 2007.

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