Pocket-Size White Noise Generator for Quickly Testing Circuit Signal Response

Q: Is it possible to generate a spectrum of all frequencies simultaneously?

A: Noise in a circuit is usually harmful, and any good circuit should output as little noise as possible. However, in some cases, a well-characterized noise source with no other signals is the desired output.

This is the case with circuit characterization. The output characteristics of many circuits can be measured by sweeping the input signal over a range of frequencies and observing the design’s response. The input sweep can consist of discrete input frequencies or a swept sine wave. Clean very low frequency sine waves (below 10 Hz) are difficult to generate. A processor, DAC, and some complex precision filtering can produce relatively clean sine waves, but the system must settle for each frequency step, making sequential full sweeps of many frequencies slow. Testing fewer discrete frequencies can be faster, but increases the risk of skipping critical frequencies where high-Q phenomena occur.

A white noise generator is simpler and faster than a swept sine wave because it effectively generates all frequencies at the same time with the same amplitude. Applying white noise to the input of the device under test (DUT) can quickly generate an overview of the frequency response over the entire frequency range. In this case, there is no need for an expensive or complicated swept sine wave generator. Simply connect the DUT output to a spectrum analyzer and observe. Using more averaging operations and longer acquisition times will produce a more accurate output response over the frequency range of interest.

The expected response of the DUT to white noise is frequency shaped noise. Using white noise in this way can quickly expose unexpected behavior such as weird frequency spurs, strange harmonics, and undesirable frequency response artifacts.

Additionally, a careful engineer can test the tester with a white noise generator. Lab equipment that measures frequency response should produce a flat noise curve when measuring a white noise generator that is known to be flat.

In practical terms, white noise generators are easy to use; small enough for compact laboratory setups; portable enough for field measurements; and inexpensive. A high-quality signal generator with a large number of settings is very flexible and attractive. However, versatility can hinder fast frequency response measurements. A well-designed white noise generator requires no controls and yet produces a completely predictable output.

Noise Discussion

Resistor thermal noise, sometimes called Johnson noise or Nyquist noise, is generated by thermal agitation of charge carriers inside the resistor. This noise is roughly white and close to a Gaussian distribution. In electrical terms, the noise voltage density is given by:

Where kB is the Boltzmann constant, T is the temperature in Kelvin, and R is the resistance. The noise voltage is caused by the random movement of charge flowing through the base resistance (roughly R × INOISE). Table 1 shows some examples at 20°C.

Table 1. Noise voltage density of various resistors

A 10 MΩ resistor represents a 402 nV/√Hz broadband voltage noise source in series with the nominal resistance. Changes in R and T affect the noise only in square root form, so the amplified resistor-derived noise source is fairly stable and can be used as a lab test noise source. For example, a change from 20°C to 6°C changes the resistance from 293 kΩ to 299 kΩ. Noise density is proportional to the square root of temperature, so a 6°C temperature change results in a relatively small change in noise density of about 1%. Similarly, for resistors, a 2% change in resistance results in a 1% change in noise density.

Consider Figure 1: A 10 MΩ resistor, R1, generates white Gaussian noise at the positive terminal of the op amp. Resistors R2 and R3 amplify this noise voltage and send it to the output. Capacitor C1 filters out the chopper amplifier charge spikes. The output is a 10 μV/√Hz white noise signal.

In this case the gain (1 + R2/R3) is higher at 21 V/V.

Even though R2 is high (1 MΩ), the noise from R2 is insignificant compared to the amplified noise of R1.

Figure 1. Complete schematic of the white noise generator. The low drift micropower LTC2063 amplifies the Johnson noise of R1.

The circuit's amplifier must have input-referred voltage noise low enough to allow R1 to be the dominant noise source. The reason is that the resistor noise should dominate the overall accuracy of the circuit, not the amplifier. For the same reason, the circuit's amplifier must have input-referred current noise low enough to avoid (IN × R2) approaching (R1 noise × gain).

How much amplifier voltage noise is acceptable in a white noise generator?

Table 2 shows the increase in noise caused by adding independent signal sources. The change from 402 nV/√Hz to 502 nV/√Hz is only 1.9 dB on a logarithmic basis, or 0.96 power dB. The op amp noise is about 50% of the resistor noise, and a 5% uncertainty in the op amp VNOISE changes the output noise density by only 1%.

Table 2. Op amp noise contributions

A white noise generator can only use an op amp without resistors that generate noise. Such an op amp must have a flat noise curve at its input. However, the noise voltage is often not precisely defined and varies greatly with production, voltage, and temperature.

Other white noise circuits may operate based on Zener diodes, but their predictability is very poor. However, finding the best Zener diode to get stable noise for μA currents can be difficult, especially at low voltages (<5V).

Some high-end white noise generators are based on long pseudo-random binary sequences (PRBS) and special filters. Using a small controller and DAC may be sufficient; however, ensuring that the DAC does not generate settling glitches, harmonics, or intermodulation products may be a task that only an experienced engineer can handle. In addition, choosing the most appropriate PRBS sequence adds complexity and uncertainty.

Low Power Zero Drift Solution

This project has two main design goals:

• An easy-to-use white noise generator must be portable, that is, battery-powered, which means it must be a micro-power electronic device.

• The generator must provide a uniform noise output, even at frequencies below 0.1 Hz and above.

Considering the above noise discussion and these key constraints, the LTC2063 low power zero-drift op amp fits the bill.

Figure 2. Pocket-sized white noise generator prototype

The noise voltage of a 10 MΩ resistor is 402 nV/√Hz, which is about half the noise voltage of the LTC2063. The noise current of a 10 MΩ resistor is 40 fA/√Hz, which is less than half the noise current of the LTC2063. With a typical supply current of 1.4 μA and a total supply voltage that can be reduced to 1.7 V (nominal voltage is 1.8 V), the LTC2063 is ideal for battery applications. Low frequency measurements, by definition, require long settling times, so the generator must be powered by the battery for long periods of time.

The noise density at the LTC2063 input is approximately 200 nV/√Hz, and the noise is predictable and flat (within ±0.5 dB) over frequency. Assuming the LTC2063 noise is 50% of the thermal noise, and the op amp voltage noise changes by 5%, the output noise density changes by only 1%.

Zero-drift op amps are designed to have no 1/f noise. Some are better than others, but more often, the broadband specifications are wrong or the 1/f noise is much higher than given in the data sheet, especially for current noise. Some zero-drift op amps have data sheet noise curves that do not drop into the MHz frequency region, perhaps to mask the 1/f noise. Chopper-stabilized op amps may be the answer, keeping the noise flat at very low frequencies. Also, high frequency noise bumps and switching noise must not detract from performance. The data shown here supports the use of the LTC2063 to address these challenges.

Circuit Description

Thin film R1 (Vishay/Beyschlag MMA0204 10 MΩ) generates most of the noise. The MMA0204 is one of the few 10 MΩ choices that is both high quality and low cost. In principle, R1 can be any 10 MΩ resistor, as the signal current is so small that the 1/f noise is negligible. For the main element of this generator, it is best to avoid low-cost thick film chips of questionable accuracy or stability.

For best accuracy and long term stability, R2, R3, or RS can be 0.1% thin film resistors, such as TE CPF0603. C2/C3 can be one of most dielectric capacitors; C0G can be used to ensure low leakage current.

Figure 3. Device layout

Deployment Details

The loop area R1/C1/R3 should be minimized to ensure the best EMI suppression performance. In addition, R1/C1 should be well shielded to prevent electric field effects, which will be further discussed in the EMI considerations section. Although not critical, R1 should be protected from large temperature changes. With good EMI shielding, thermal shielding is often sufficient.

The LTC2063 rail-to-rail input voltage transition region within the VCM range should be avoided as crossover may generate higher and less stable noise. For best results, use at least 1.1 V for V+ and an input common-mode voltage of 0.

Note that an RS of 10 kΩ may seem high, but the micropower LTC2063 has a high output impedance, and even 10 kΩ will not completely decouple the LTC2063 from the load capacitance at its output. For this white noise generator circuit, some output capacitance that causes peaking can be a design feature rather than a hazard.

The output sees 10 kΩ RS and a 50 nF capacitor CX to ground. This capacitor CX will interact with the LTC2063 circuitry to cause peaking in the frequency response. This peaking can be used to extend the flat bandwidth of the generator, just like the hole in a megaphone widens the bottom end. A high impedance load (>100 kΩ) is assumed, as a low impedance load will significantly reduce the output level and may also affect the peaking.

Optional tuning

In the high frequency limit, several IC parameters such as ROUT and GBW affect flatness. If a signal analyzer is not used, the recommended value for CX is 47 nF, which typically yields a bandwidth of 200 Hz to 300 Hz (-1 dB).