Audio Noise Figure Meter

Transcription

1 Audio Noise Figure Meter Abstract Low noise amplifiers in the audio range are used in many applications. The definition of 'lownoise' is very flexible and poorly defined so any experimenter in this field needs to measure exactly how much noise is being generated in the amplifier. This project describes an instrument which measures the relative noise figure of audio amplifiers. The LM3S811 microprocessor on the Luminary Stellaris LM3S811 Evaluation board was the basis for the instrument. Additional circuitry was designed and built to accomplish the goal. I do not know of any commercial instruments which make the same measurement. Introduction All active devices generate internal noise. For an amplifier, this internal noise signal is added to the desired input signal so the output of the amplifier always has a S/N ratio which is less than that at the input. In the case of amplifiers in the low end of the audio region of the spectrum, this noise is generally quite high due to the presence of shot and flicker noise. In recent years, with the advent of many new consumer audio devices, there has been a plethora of new components designed for use in low-noise amplifiers. The specifications of these devices are often abbreviated and difficult to interpret. It is often necessary to build a circuit to see how they perform for any given amplifying application. But, how is one to tell how good the finished amplifier is? The answer to this question is to build an instrument to actually characterize the observed amplifier noise in the audio region - and that was the object of this contest entry. Theory Any amplifier may be thought of as if it was the combination of a perfect amplifier which does not generate any noise plus an internal noise source at the input which adds noise to the external signal. The equivalent circuit of this is shown in Figure 1. Here, I have represented the internal noise generator as a resistance because all resistors generate thermal noise with a power/unit bandwidth, P n, given by: P n = kt n where k is Boltzmann's constant which is and the temperature is in Kelvins. P n is in units of Watts/Hz. This 1

2 representation is convenient because we can use the temperature, T n, to characterize the amount of noise generated by the amplifier. A poor, high-noise level, amplifier would have a higher noise temperature than a better, lower-noise amplifier. This way describing the noise performance of an amplifier is common in RF applications. Another way of describing the same noise temperature is the noise figure which is just the noise temperature plus room temperature divided by room temperature. If the amplifier in Figure 1 has a power gain of G, then the output power/unit bandwidth delivered by the amplifier to its load, P o, will be: P 0 = G( P n + P s ) where P s is the signal power. Normally, we want P n to be as low as possible, especially if P s is small. The instrument to be described is one which gives some measure of P n for any given amplifier. Theory of Measurement Technique I have constructed this instrument in a manner analogous to that used for RF measurements of noise figure. For RF applications, the instrument is often called an Automatic Noise Figure Indicator (ANFI). It consists of a bandlimited amplifier appropriate to the frequency of the amplifier being investigated plus a broad-band noise source which can be switched on and off rapidly. A block diagram of such an instrument, connected to a device-undertest (DUT) is shown in Figure 2. The noise source consists of a specially constructed Zener diode followed by an attenuator. When a current passes through it, it generates broad-band noise and so appears as a resistor with a high temperature, T h, and when the current is turned off, it appears as a resistor at room temperature, T c. The noise source is turned on and off repeatedly and the output of the RF power meter is detected synchronously giving the power output levels when the noise source is on and when it is off. This ratio of these two is called the Y factor. For a device under test which has a noise temperature of T n, Y will be, approximately: ( Th + Tn ) Y = T + T ( ) c n 2

3 This equation is an approximation because the noise generated by the amplifier following the DUT will also contribute to the output noise when the noise source is both on and when it is off. If the gain of the DUT is reasonably high, the factor Y is a good measure of how low the noise of the DUT. The lower the T n of the DUT, the higher the measured Y will be. In a commercial ANFI, both the hot temperature and the cold temperature of the noise source are known as is the noise figure of the amplifier following the DUT. Knowing these factors, it is possible to calculate and display the value of both the gain of the DUT and T n. The Instrument The instrument I built has the block diagram shown in Figure 3. The heart of it is the LM3S811 Evaluation Board (EVB) which acts as both the audio noise generator and the synchronous power detector. As a low-noise amplifier (LNA) 'standard', I built a single stage amplifier using one half of the LM394 super-matched transistor pair. This device is a very low-noise amplifier when the transistor is biased to about 0.1 ma of collector current. The circuit diagram for this amplifier is shown in Figure 4. I measure the value of Y for this amplifier and use it as a standard of comparison for other amplifiers. If they give a value of Y which is higher than that for this standard, then they are better and have lower noise-figures. If they give a value of Y which is less, then they are worse. This instrument is not completely comparable to the RF ANFI because it only allows a comparative measurement to be made; a comparison to my 'standard' LNA. However, this is extremely useful in selecting components for amplifiers. I will describe later how the instrument may be improved to allow it to make absolute measurements. Design Criteria There were several criteria selected prior to the final design: 1 The bandwidth was to be determined by passive L-C filters at both the input to the DUT and at the input to the ADC of the microprocessor, 2 The sample rate of the ADC was to be high enough to measure all the energy in the pass band, 3

4 3 The program length was to be less than the 16K limit for the free Keil evaluation software so that others could replicate and alter the design without having to buy a license, 4 The instrument should display a running average of Y so that the effects of circuit adjustments can be seen readily. Design Considerations RF measurements are made with instruments designed for specific input and output impedances; most often 50 Ohms but sometimes 75. Audio measurements are most often measured using input and output impedances of 600 Ohms and that is what I chose to use in this instrument. The exact audio range to use for the noise measurement is a matter of choice. I am interested in building proton magnetometers and the proton precession signal is a very weak narrow-band signal in the vicinity of 2 KHz so I wanted to include this frequency in the range of the instrument. Most voice and instrumental energy is contained at frequencies roughly lower than 4 KHz so I arbitrarily chose this as the upper limit and, also arbitrarily, I chose 250 Hz as the lower limit. The noise signal was generated using a pseudo-random sequence which was fed into the pulsewidth modulator (PWM). The output of the PWM will contain, in addition to the frequency at which it is clocked, components at frequencies up to ½ the rate at which the PWM is refreshed. I chose to make this rate 8 KHz so that the pseudo-random sequence, before filtering, would contain components between 0 and 4 Khz. The band-pass filter after the PWM was designed to be a Chebyshev low-pass 0.5 db ripple filter with a corner frequency of 3.5 KHz and a characteristic impedance of 600 Ohms. This 7-pole filter has a very rapid cut-off and the response is down some 40 db at 4 KHz. The lowfrequency cut-off would be determined by the coupling capacitor of the output of the DUT. Another filter of identical design is used at the anti-aliasing filter at the input to the ADC. The output of the PWM filter goes to an attenuator to give the desired low level signal to feed to the DUT. It consists of three sections of a T-type attenuator. The first and last stage have a characteristic impedance of 600 Ohms and an attenuation of about 15. The middle stage was modified to increase the attenuation with a consequent change in the characteristic impedance of the stage. However, the final input and output stages will still look very to be very close to 600 Ohms in impedance. The overall attenuation of this three-stage attenuator is a factor of about The amplifier used between the DUT and the anti-aliasing filter is one which uses two stages of the LM394 low-noise NPN transistor. Each stage is biased to operate at about 0.09 ma and the overall voltage gain of this amplifier is about The high output impedance of the basic two-stage amplifier (about 22K) is transformed to a lower impedance by an emitter-follower stage before going into the anti-aliasing filter. Because the amplifier gets its +5V power from the USB port of the computer which powers the EVB, it is very important that no power-supply switching noise get into this high-gain amplifier. Accordingly, the +5V to the amplifier is filtered through a two-stage LC filter, each stage consisting of a 33 mh inductor going to a 100 microf capacitor to ground. This amplifier has a lot of gain and it was built carefully taking into account all considerations for stability and low noise. For example, all circuit grounds were connected to a single point going to chassis ground. To measure the noise output power of the band-limited signal, it is necessary to measure power through the full spectrum for about 250 Hz to 4 KHz. At RF, there are wonderful IC's which have a dynamic range of some 80 db to do just that. In my case, the signal is in the audio range and so I chose 4

5 to do it with one of the ADC inputs to the microprocessor. From Nyquist's Theorem, to completely characterize a signal containing components up to 4 KHz, it is only necessary to sample the signal at twice that upper limit; 8 Khz. The output of the amplifier was at a DC level of about 1.6V which is roughly near the middle of the ADC range. This signal was sampled at 8 KHz using the ADC input #1 (ADC input #0 is used on the EVB to sample the potentiometer on the board). The complete circuit diagram of the completed instrument is shown in Figure 5. For lowest noise, in both the standard LNA and in the two-stage amplifier, all resistors were metal film. Carbon or carbon film resistors contribute some excess noise. The Program The program uses a single timer interrupt routine which is set to be interrupted at an 8 KHz rate. In this interrupt routine, the PWM is refreshed with a new random number and a sample is taken when the instrument is in its NOISE ON phase. In the NOISE OFF phase, the samples are still taken but the PWM output is held constant so that no noise signal is generated. The sampled data is stored in an array and, for each phase of the measurement sequence, the average DC component of the ADC samples is subtracted from the array and then the sum of the squares of the remainders is calculated. This sum is a measure of the total noise power received at the input of the ADC during the sampling interval. After each NOISE ON/NOISE OFF sequence, a value of Y is calculated as the ratio of NOISE ON power to NOISE OFF power. This is displayed as a running average on the OSRAM display with a time constant of 8; that is, the value displayed is 7/8 of the previous value plus 1/8 of the new one. The array size originally chosen was 1024 floating point samples which uses half the available RAM storage for this particular microprocessor. I chose this number because I wanted to calculate the Fast Fourier Transform (FFT) in order to examine the spectrum of the digitized samples. Including the FFT in the program increased the program size to greater than 16K so it was, in the final version, left out. When no FFT was being done, I increased the array size to 1536 samples just to get a larger array of samples. When this instrument is operating, because it samples at 8 KHz, it takes roughly 0.18 seconds to fill the array so a single complete measurement takes about 0.36 seconds. The subsequent calculations take a trivial amount of time so the whole instrument makes about 3 measurements per second. As an aside, calculating a 1024 point Fourier Transform also is very rapid with this microprocessor! Because the 'signal' is noise, there is some significant scatter from one measurement to the next and even the running average shows statistical fluctuations with time. Therefore I included, in the program, provision to measure the average Y over 100 complete measurements. This is initiated by a command from the keyboard of a computer connected to the UART in the EVB via the USB cable. I also wanted to differentiate between these computed values between the case where the 'standard' LNA was in place (a 'calibration' measurement) and when the DUT was in place. So there are two separate keyboard commands to initiate one or the other of these measurements. In both cases, after the 100 measurements have been taken, the average POWER ON power, the average POWER OFF power and the average Y are sent out the UART port to the computer for subsequent storage. An example section of the code, the function which returns the measured power over the sampling interval, is shown in Listing 1 at the end of this document. Photo 1 is a photograph of the instrument as built. The EVB was mounted, on standoffs, over a piece of double-sided pc-board. The external circuit, the filters, and attenuator were constructed on pads made on the top surface of the pc-board with a Dremel tool. The two-stage amplifier was cut from 5

6 a previously constructed project which had been carefully laid out on a pc-board. Photo 2 shows the standard LNA which plugs into the terminals provided to connect the instrument to a device being tested. Second Thoughts This instrument works and is useful but it is very much a proof of concept rather than a finished instrument. Using it has shown that a finished instrument would need to have some changes. Firstly, the layout needs to be improved. The signal coming out from the attenuator is at a very low level about 1 µv rms. As laid out here, the output of the attenuator is too close to the input circuitry of the two-stage amplifier and I suspect that there is some stray coupling bypassing the DUT. In a second version of this instrument, I would shield both the noise generating portion of the circuit and the amplification portion of the circuit following the DUT. Secondly, the attenuator provides a lot of attenuation and it is too compressed in layout to prevent stray coupling between input and output. A better layout would make use of four or more stages of attenuation spaced over a larger area and with better shielding between input and output. This would allow an accurate value of attenuation to be calculated. With these provisions, it would be possible to calculate the actual noise temperature of the source by sampling the signal at the input to the attenuator (in exactly the same way the output of the amplifier is sampled) and thereby calculating, exactly, the noise power going into the DUT when the noise was turned on. With this absolute measurement, both the noise figure and the gain of the DUT could be calculated. As it is, I measured the rms input voltage to the input of the attenuator with my trusty old Fluke 75 meter. This meter does not measure true rms and I suspect that it doesn t respond to the higher frequency components but it gave a value of 0.159V at the input to the attenuator. Using this number and the calculated attenuation, this meant that the noise signal going into my standard LNA had an amplitude of about 1.5 µv rms. The observed value of Y was 34 and, working through the numbers, the noise generated inside the LM394 came out to within a factor of two or three to the data sheet number of 1.8 nv/hz 1/2. With the changes recommended above, it should be possible to do this 6

7 operating correctly. sort of calculation much more precisely. Another useful change in a finished instrument would be to have several band-pass filters selectable for different purposes. If one wanted to make a low-noise amplifier suitable for hi-fi uses, the bandwidth should really be increased. The microprocessor is sufficiently fast that samples up to 40 or 50 K samples per second are feasible so the broad-band noise over a width of more than 20 KHz is possible. Improvements could also be made in the program. If one were to disregard the selfimposed limit to the size of the code, adding a FFT calculation is a very useful, and in my opinion essential, thing to do. Examination of the output spectrum of the DUT shows whether the device is Photo 3 shows the standard LNA mounted onto the instrument when it is connected to the USB port which powers the instrument. This is a poor photo taken in poor lighting but it shows the OSRAM display giving the value for Y for this amplifier. 7

8 float MeasurePower(void) { int i; float sum; gpointer = 0; // point to the beginning of the data array gfasttick = 0; // restart Tick clock while (gtick < 10); // wait 10 ms before starting digitizing gadcstarted = true; while(gadcstarted); // start collecting data into the array //.. and wait here till it is done sum = 0.0; for(i = 0; i < DATASETSIZE; i++) sum += gdata[i]; sum /= (float) DATASETSIZE; for(i = 0; i < DATASETSIZE; i++) gdata[i] -= sum; sum = 0.0; for(i = 0; i < DATASETSIZE; i++) sum += (gdata[i] * gdata[i]); sum /= (float) DATASETSIZE; return sum; } // mean is now removed // power is proportional to amplitude squared Listing 1. The MeasurePower() function. gdata[] is the array where the A/D samples are stored after being converted to floating point variables. The array is filled with samples in the Timer0 interrupt routine and, when it is full, the global variable, gadcstarted, is set to false to both stop the A/D conversions and to indicate to the rest of the program that the data sampling period is over. 8

9 Figure 4. Schematic of standard LNA 9

10 1