White Noise Generator - · PDF file04.08.2008 · Electronic Circuits II Project...

UNIVERSITY OF TEXAS AT SAN ANTONIO

White Noise Generator Circuitry and Analysis

David Sanchez

8/4/2008

Electronic Circuits II Project – White Noise Generator Page 2

Table of Contents Introduction .................................................................................................................................................. 3

Overview of the Circuit ................................................................................................................................ 3

Circuit Subsets .............................................................................................................................................. 4

Noise Generation Stage ........................................................................................................................ 4

Amplification of the Noise Signal .......................................................................................................... 6

Active Low-Pass Filter ........................................................................................................................... 7

Audio Output Stage............................................................................................................................... 8

Analysis ......................................................................................................................................................... 9

Discussion ................................................................................................................................................... 11

Conclusion .................................................................................................................................................. 12

Works Cited ................................................................................................................................................ 13


Introduction

A white noise generator is just that – a circuit that produces white noise. White noise

is essentially just distortion whose amplitude is constant through a wide frequency

range. It is often produced by a random noise generator in which all frequencies are

equally probable, just as white light is composed of all the colors of the visible light

spectrum. The human hearing range is from approximately 20Hz to 20,000Hz. In this

range, the human ear is more sensitive to the higher frequencies. Due to the fact that it

incorporates all sound frequencies - from low, deep sounds to very high sounds - it has

a very beneficial noise cancelling or masking effect. This noise finds applications in the

medical, social, and technological fields. It is a gentle tone that can be found in nature,

and the actual sound produced is comparable to rainfall or ocean waves.

Overview of the circuit

The circuit that produces white noise is fairly simple in nature. It consists of four

stages or fragments – noise generation, signal amplification, low-pass filter, and audio

output stage. A flow chart of the circuit is shown in Figure 1. The circuit uses all

discrete parts that are both active and

passive. The active devices are the LF411

and LM386 operational amplifiers and the

passive components are the resistors and capacitors. There are no inductors in this

circuit. We decided to use op-amps for amplification because of the many advantages

they have over discrete transistors, the most noticeable are “high efficiency, high gain,

low standby power, low component count, small size and, of course, low cost” (Martell).

The noise is generated from a pair of npn bipolar junction transistors that are tied

Noise

GenerationAmp

Active Low-pass

Filter

Circuitry to

Speaker

Figure 1


together at their base terminals. This basically creates a zener diode and it is biased in

the reverse breakdown region of operation. Being operated in this region, the pn

junction starts to exhibit the zener breakdown phenomenon, and as such produces shot

noise and creates a low-level, constant amplitude distortion signal. The noise

generation stage is ac coupled to the amplification stage so as to pass the distorted

signal but block the dc signal. The amplifier is set up in an inverting configuration which

uses a negative feedback loop. This negative feedback helps to stabilize the output

even further and helps to protect the signal from any spike that might occur. The gain of

this amplifier stage is Av=100, and is 180˚ out of phase, as shown in the next section.

The output of the amplification stage is then passed through a low-pass filter (LPF).

Since human hearing ranges from 20Hz to 20kHz, the filter is design to pass these first

20kHz and block the higher (useless) frequencies. The cutoff frequency was design to

be approximately 13kHz, with a -40dB/decade decrease thereafter. The passed signal

from the LPF then enters an audio output stage. This stage basically amplifies the

signal to a level that can be output through a speaker. The next section describes each

of the stages in more depth and shows the circuit schematic for each fragment.

Circuit Subsets

Noise Generation Stage

The first stage in our circuit is noise generation, where the constant power output

is produced. We decided to generate noise with the zener breakdown

phenomenon. Zener breakdown occurs when a zener diode is run in the reverse-

breakdown region of operation. This usually occurs when approximately -1mA of

current is passed through the diode. At this current level the zener diode enters


reverse breakdown and the current through it drops rapidly while the voltage

across it remains relatively constant. This

voltage level is termed zener voltage and

is represented by VZ. The I-V plot showing

this phenomenon is shown in Figure 2.

The noise generated while operating a

zener diode in this region is based on the

avalanche breakdown that occurs in the pn

junction. In our circuit we actually did not use a zener diode but instead two npn

bipolar transistors. These two transistors are tied together at their bases and

connected to the same power supply. One of the BJTs is connected to the power

supply at its collector terminal and tied to ground at the emitter. The other BJT is

connected to the power supply at its emitter terminal and the collector terminal is

floating. This essentially creates a pn junction all the same as

a zener diode. The next step in the generation process was to

make sure that we were operating the transistors (pn junction)

in the reverse breakdown region. This was accomplished by

applying a +15VDC supply as power. To protect the power

supply we put a 4.7k resistor in series with the transistors.

We also put a 1uF capacitor from +15V to ground as a

blocking cap. This basically makes up the noise generation

stage of the circuit. The circuit schematic of this stage is shown in Figure 3.

Figure 2

Q2

1uF

4.7k

0

Q1

0

Vs

up

ply

15V

Figure 3


Amplification of Noise Signal

The next step in white noise generation is to amplify the very low noise that is

produced by the transistors running in reverse breakdown. This was

accomplished by using an operational amplifier with negative feedback. We

decided to use a LF411 as the amplifier because of its extremely high open-loop

gain (~250,000) and high input impedance

(>106 Ω). Both of these are large enough to

consider infinite, therefore ideal op-amp

analysis was used. One of the major non-ideal

characteristic of this amplifier is that the output

of the circuit cannot go past the power supply

rails, plus-or-minus fifteen volts in our case.

This is okay though because the noise

generated and output is orders of magnitude

smaller than 15V, and therefore we ignored this

shortcoming. Using negative feedback we were able to control the gain of the

411 externally. We wanted a gain of approximately 100 so we used a 1kΩ

resistor at the inverting terminal of the op-amp and used a 100kΩ resistor from

the output (pin 6 for the LM411) back to the inverting terminal. In doing so we

created an inverting amplifier with the gain of:

AV = –R2/R1 = -100k/1k = 100

The non-inverting terminal of the op-amp was grounded through a 1kΩ. The

circuit schematic of this stage is shown in Figure 4.

1uF

100k

1k

0

15V

1k

15V

U1

LF411

3

2

74

6

1

5+

-

V+

V-

OUT

B1

B2

0

0

Figure 4


Active Low-Pass Filter

Once the low-level noise is amplified it needs to be tailored to output over the

frequencies of interest, 0Hz to 20kHz in our case (human hearing range). To

accomplish this we designed an active low pass filter with a cutoff frequency of

13kHz. It is termed “active” because it uses an op-amp instead of just passive

components such as resistors, capacitors, and inductors. The circuitry of this

LPF is shown in Figure 5. The op-amp we used to

implement this filter was again an LF411. This

time however it had both positive and negative

feedback, allowing us to customize the output

characteristics. The first decision we had to make

was whether or not to have gain with this amplifier.

Since we had a dedicated stage just for

amplification of the noise, we decided to set it up

as a voltage follower, giving us unity gain over the

frequency range of interest. It also provides high

input impedance and very low output impedance.

At low frequencies (<<13kHz) the filter passes the noise generated by the

transistors. At frequencies above 13kHz the filter exhibits a two-pole roll-off,

falling approximately 40dB/decade. This is desirable because humans cannot

hear frequencies above 20kHz. The transfer function of the active low-pass filter

includes a Q term which describes the peak response and bandwidth. For a Q

larger than 0.71, the filter exhibits a peaked response that is usually undesirable,

15V0

0

R10

1k

62k

200pF

62k

0

200pF

R9

1k

0

U2

LF411

3

2

74

6

1

5+

-

V+

V-

OUT

B1

B2

15V

Figure 5


whereas a Q below 0.71 does not take maximum advantage of the filter’s

bandwidth capability. This is a direct implication of the gain-bandwidth product.

Increasing bandwidth comes at the cost of gain, and vice-versa. We chose to

design for a Q equal to 0.71 to maximize bandwidth without a peak response. As

mentioned earlier, active low-pass filters use positive and negative feedback.

“The filter uses positive feedback through [the capacitor from the output of the

411 to the non-inverting terminal] at frequencies above dc to realize complex

poles without the need for inductors” (Jaeger and Blalock 571). Negative

feedback comes from the output, through the voltage divider, and back to the

inverting terminal. The 56k resistor and the 100k resistor set the Q-point of the

filter, and since there is a path to ground the op-amp’s gain is not affected

(voltage follower).

Audio Output Stage

The last stage of the circuit is an audio amplifier. We chose to use an LM386-1,

which has an output power level of 300mW. These are widely available op-amps

and can be operated as low as five volts. One unique aspect of these audio

amps is the gain can be modified by connecting a resistor and capacitor from pin

one to pin six. As with the LF411, increasing gain comes with lower output power

and should only be used when the input level is extremely low. The non-inverting

terminal is connected to a 10k potentiometer, which is itself connected to the

output of the LPF stage and ground, and becomes the input to the amplifier. The

potentiometer controls the gain of the LM386 externally. The inverting terminal is

then connected to ground. The power supplied to the op-am is +15V and 0V, and

as before to protect the proto-boards internal power supply, we put a 10Ω resistor


in series and a 220μF electrolytic capacitor to ground. This becomes a blocking

capacitor and is discussed in the first paragraph of this section. The output of this

amp goes through a 220μF coupling capacitor and on to the speaker to output the

desired white noise. The speaker itself is a two-wire device in which one input

comes from the LM386 and the other is tied to ground.

Analysis

As we finished the

construction of our

circuit, we began

analyzing at multiple

nodes, hoping for

desirable results. Our

completed schematic

can be seen in Figure 6.

To check the various

outputs, we used an oscilloscope and a dynamic signal analyzer on our

protoboard.

Q2

1uF

3.3k

15V

4.7k

0

1uF

Rspeaker

8

0

Vout

10

0

0

0

15V

Q1

1k

0

R10

1k

62k

220uF

0

200pF

0

0

220uF

62k

0

+

-

LM386/SO

3

25

6

14 87

0

15V

200pF

R9

1k

0

1k

Vsupply

15V

3 1

2

U1

LF411

3

2

74

6

1

5+

-

V+

V-

OUT

B1

B2

15V

0

100k

U2

LF411

3

2

74

6

1

5+

-

V+

V-

OUT

B1

B2

15V

0

Figure 6


We checked the output at the final

stage of the circuit, as shown in

Figure 7. This plot shows a relatively

constant noise being output in our

desired range of frequencies (from

0Hz to around 20kHz; audible range).

Roll-off due to the LPF stage is also

visible at the 13kHz we designed for

in this screenshot. Unfortunately, we

were unable to hear any white noise output from the speakers. We concluded

that this was due to a lack of

amplification of the noise signal in the

amp stage of our circuit. Moving

backward a node we then took an

oscilloscope screenshot and dynamic

signal analyzer plot of the output of the

active low-pass filter stage is shown in

Figure 8. At this node we were able to

successfully generate white noise and in

Figure 8a you can visibly see the low-

pass filter roll-off we hoped for.

Unfortunately the frequency range of

constant power was significantly lower

Figure 7

Figure 8 (a) Dynamic Signal Analyzer (top) and (b)

Oscilloscope (bottom)


than expected. The corner frequency is approximately 5kHz, which is 8kHz less

than we designed for. Comparing Figure 7 and Figure 8a it is shown that the

output level of the LPF stage is much larger in amplitude than the output of the

audio stage. For some reason (probably the LM386 itself) there was significant

signal attenuation in going through the last stage, and this attenuation dropped

the output level too low to be picked up by the speaker. The output amplitude

level of the LPF stage was approximately 0.05mV, more than enough to power

the speaker and output noise.

Discussion

We ran into a couple of problems

during our analysis of our physical

circuit - including lack of amplification

and signal attenuation which dropped

our signal. A solution to the problem

of no sound output out of the final

stage is to add a second amplification

stage to the circuit. Because

amplification is dependent on resister

value ratios of the negative feedback

loop, they must be adjusted to create a larger ratio; thus a larger amplification.

Installing a higher sensitivity speaker to pick up the very low output signal is also

an option.

Figure 9


Looking back on our design we realized that we were possibly “over gaining”

our amplification stage and thereby affectively decreasing our potential

bandwidth. The early roll-off could also be due to the amp stage LM411’s

internal capacitance. It was earlier stated that as you increase gain you lose

bandwidth, and vice-versa. We designed for a gain of 100, and in return lost

most of our desired bandwidth. This can be seen in Figure 9, which is a dynamic

signal analysis of the output of the amplification stage.

Conclusion

In the end we were able to successfully compensate and make adjustments

to generate white noise. We ended up having to scrap our audio output stage

and directly connect the speaker to the output of the active low-pass filter. This

was a fairly easy to build circuit due to the basic component and was a definite

learning experience.


Works Cited

"Building a Low-Cost White-Noise Generator." Maxim. 14 Mar. 2005. 05 Apr. 2008

<http://www.maxim-ic.com/appnotes.cfm/appnote_number/3469>.

"Capacitors Blocking DC." All About Circuits. Feb. 2006. 15 Apr. 2008.

"Capacitor Types and Colors." Elecraft. 20 Apr. 2008

<http://www.elecraft.com/Apps/caps.htm>.

“Colors of noise.” Wikipedia, The Free Encyclopedia. 4 May 2008, 22:40 UTC. Wikimedia

Foundation, Inc. 7 May 2008 < http://en.wikipedia.org/wiki/Colors_of_noise>.

Costello, Carol. "The Basics of Making a Presentation." Electrical Engineering Dept. University of Texas

At San Antonio, San Antonio. Apr. 2008.

Hansen, Lars. Electrical Engineer Lab 1. University of Texas At San Antonio, San

Antonio. Spring 2008.

Horowitz, Paul, and Hill Winfield. The Art of Electronics. New York: Cambridge UP, 1989.

Introduction to Op Amps. Dept. of EE., Swathmore University. 03 May 2008

<http://www.swarthmore.edu/NatSci/echeeve1/Class/e72/E72L2/Lab2(OpAmp).html>.

Martel, Mike. "Integrated Circuit Audio Amplifiers." 04 May 2008

<httl://www.rason.org/Projects/icamps/icamps.htm>.

Ortiz, John. Electronic Circuit II. University of Texas At San Antonio, San Antonio.

Summer 2008.

Sound Masking Systems. Avlelec. 20 Apr. 2008

<http://www.avlelec.com/PDFs/soundmasking_whitepaper.pdf>.

"Tiny White Noise Generator." Web-Ee. 15 Apr. 2008 <http://web-

ee.com/schematics/noise_generation/pseudo-random-white-noise/>.

http://en.wikipedia.org/wiki/Colors_of_noise


"White Noise Generator." Waynesrngcomp. 5 Apr. 2008

<http://world.std.com/~reinhold/waynesrngcomp.gif>.

"Wide-Band Analog White-Noise Generator." Electronic Design. 3 Nov. 1997. 20 Apr. 2008

<http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=6356>.

Wisniewski, Joseph S. "The Colors of Noise." Product Technology Partners. 07 Oct. 1996. Ford

Motor Company. 18 Apr. 2008 <http://www.ptpart.co.uk/show.php?contentid=71>.

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