White Noise Generator

Transcription

1 UNIVERSITY OF TEXAS AT SAN ANTONIO White Noise Generator Circuitry and Analysis David Sanchez 8/4/28

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 Conclusion Works Cited Electronic Circuits II Project White Noise Generator Page 2

3 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 2Hz to 2,Hz. 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 Noise Generation Amp Active Low-pass Filter Circuitry to Speaker passive. The active devices are the LF411 Figure 1 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 Electronic Circuits II Project White Noise Generator Page 3

4 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 A v =1, and is 18 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 2Hz to 2kHz, the filter is design to pass these first 2kHz and block the higher (useless) frequencies. The cutoff frequency was design to be approximately 13kHz, with a -4dB/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 reversebreakdown region of operation. This usually occurs when approximately -1mA of current is passed through the diode. At this current level the zener diode enters Electronic Circuits II Project White Noise Generator Page 4

5 Vsupply 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 V Z. 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 Figure 2 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 +DC supply as power. To protect the power 4.7k 1uF supply we put a 4.7k resistor in series with the transistors. Q1 Q2 We also put a 1uF capacitor from + to ground as a blocking cap. This basically makes up the noise generation Figure 3 stage of the circuit. The circuit schematic of this stage is shown in Figure 3. Electronic Circuits II Project White Noise Generator Page 5

6 4 V- V+ 7 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 (~25,) and high input impedance (>1 6 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 1uF U LF411 B2 OUT B rails, plus-or-minus fifteen volts in our case. This is okay though because the noise generated and output is orders of magnitude Figure 4 smaller than, 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 1 so we used a Ω resistor at the inverting terminal of the op-amp and used a Ω 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: A V = R 2 /R 1 = -/ = 1 The non-inverting terminal of the op-amp was grounded through a Ω. The circuit schematic of this stage is shown in Figure 4. Electronic Circuits II Project White Noise Generator Page 6

7 4 V- V+ 7 Active Low-Pass Filter Once the low-level noise is amplified it needs to be tailored to output over the frequencies of interest, Hz to 2kHz 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 2pF implement this filter was again an LF411. This time however it had both positive and negative 62k 62k 2pF U LF411 B2 OUT B R9 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 R1 amplification of the noise, we decided to set it up as a voltage follower, giving us unity gain over the Figure 5 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 4dB/decade. This is desirable because humans cannot hear frequencies above 2kHz. 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.71, the filter exhibits a peaked response that is usually undesirable, Electronic Circuits II Project White Noise Generator Page 7

8 whereas a Q below.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.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 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 3mW. 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 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 + and V, and as before to protect the proto-boards internal power supply, we put a 1Ω resistor Electronic Circuits II Project White Noise Generator Page 8

9 Vsupply Rspeaker 4 4 V- V- V+ V in series and a 22μF 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 22μF 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 1 22uF construction of our 2pF circuit, we began analyzing at multiple nodes, hoping for 4.7k 1uF U LF411 5 B2 6 OUT 1 B1 62k 62k 2pF U B2 2 - LF411 6 OUT 1 B R9 3.3k LM386/SO 22uF Vout 8 desirable results. Our 1uF R1 Q1 Q2 completed schematic can be seen in Figure 6. Figure 6 To check the various outputs, we used an oscilloscope and a dynamic signal analyzer on our protoboard. Electronic Circuits II Project White Noise Generator Page 9

10 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 Hz to around 2kHz; audible range). Roll-off due to the LPF stage is also visible at the 13kHz we designed for in this screenshot. Unfortunately, we Figure 7 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 lowpass filter roll-off we hoped for. Unfortunately the frequency range of Figure 8 (a) Dynamic Signal Analyzer (top) and (b) Oscilloscope (bottom) constant power was significantly lower Electronic Circuits II Project White Noise Generator Page 1

11 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.5mv, 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 Figure 9 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. Electronic Circuits II Project White Noise Generator Page 11

12 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 1, 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. Electronic Circuits II Project White Noise Generator Page 12

13 Works Cited "Building a Low-Cost White-Noise Generator." Maxim. 14 Mar Apr. 28 < "Capacitors Blocking DC." All About Circuits. Feb Apr. 28. "Capacitor Types and Colors." Elecraft. 2 Apr. 28 < Colors of noise. Wikipedia, The Free Encyclopedia. 4 May 28, 22:4 UTC. Wikimedia Foundation, Inc. 7 May 28 < Costello, Carol. "The Basics of Making a Presentation." Electrical Engineering Dept. University of Texas At San Antonio, San Antonio. Apr. 28. Hansen, Lars. Electrical Engineer Lab 1. University of Texas At San Antonio, San Antonio. Spring 28. Horowitz, Paul, and Hill Winfield. The Art of Electronics. New York: Cambridge UP, Introduction to Op Amps. Dept. of EE., Swathmore University. 3 May 28 < Martel, Mike. "Integrated Circuit Audio Amplifiers." 4 May 28 <httl:// Ortiz, John. Electronic Circuit II. University of Texas At San Antonio, San Antonio. Summer 28. Sound Masking Systems. Avlelec. 2 Apr. 28 < "Tiny White Noise Generator." Web-Ee. 15 Apr. 28 < Electronic Circuits II Project White Noise Generator Page 13

14 "White Noise Generator." Waynesrngcomp. 5 Apr. 28 < "Wide-Band Analog White-Noise Generator." Electronic Design. 3 Nov Apr. 28 < Wisniewski, Joseph S. "The Colors of Noise." Product Technology Partners. 7 Oct Ford Motor Company. 18 Apr. 28 < Electronic Circuits II Project White Noise Generator Page 14