In an oscilloscope display, vertical resolution can often be dramatically improved by conditioning the signal. This conditioning can take place either inside or outside of the instrument.
The most significant impediment to vertical resolution is noise. Electronic circuits, conductors, and devices introduce a certain amount of noise which adds to the signal of interest. Consequently, the oscilloscope display is sometimes not a sufficiently accurate representation of the original signal.
Consider the common resistor. It is a passive, two-leaded device. When voltage is applied across a resistor, current flows through it. The amount of current is limited by the value of the resistance in accordance with Ohm’s law and energy dissipates in the form of heat, quantified as I2R.
Now consider a resistor that is grounded at one end with the other end not connected to anything. Because there is no external power source, it would appear that no current flows through the resistor. But in actuality, there is a measurable amount of current. And because there is a definite resistance, voltage drop appears across the resistor, which is at once the source and the load.
It is hard to imagine current flowing through the resistor because one end is not terminated, but this is the case. The current is a consequence of random motion of the numerous free electrons within the resistor. They continually collide with one another and with the inner wall of the resistor package. The electrons are charge carriers, so current flows through the dead-ended device.
The reason why can be seen if we graph the electrical energy at the resistor. It will be seen that despite the fact that there is electrical energy at all times, half of it is below the X-axis and half of it is above the X-axis. The average, non-instantaneous amount of electrical energy is zero. Remember we are graphing electrical energy, not amplitude in volts as in an oscilloscope operating in the time-domain mode.
Electrical noise, or Johnson-Nyquist noise, is thermal in nature. It is proportional to the temperature above absolute zero and also to the bandwidth. Thermal noise was measured by John Johnson in 1926 and subsequently interpreted by Harry Nyquist at Bell Labs.
Johnson-Nyquist noise is distinct from shot noise, which is an electrical overlay that accompanies thermal noise when a switch is thrown so as to initiate current flow. Johnson-Nyquist noise is also called white noise because the amount of power is constant at all frequencies up to about 50 GHz. Because noise has a strong tendency to obscure a signal of interest, investigators implement measures to eliminate it from the equation. This can take place either prior to the point of connection or inside the instrument.
Often a large fraction of the noise has a higher frequency than that of the observed signal. If this is the case, the noise can be substantially eliminated by connecting a capacitor in parallel with the input, shunting the noise to ground. The capacitance (as well as working voltage) must be carefully chosen so as to reduce the noise without affecting the signal. The same end result can be accomplished by placing an inductor in series with the signal.
Another way of reducing thermal noise at the source is to cool the device or circuitry where the noise originates. Astrophotographers use digital cameras incorporating charge-coupled device (CCD) sensors that experience noise-related problems. In the course of long exposures, noise originating in the sensor accumulates and manifests as small speckles in the digital image.
Unfortunately these pinpoints of light resemble stars, thereby introducing false astronomical data. To mitigate this problem, CCD-based digital cameras incorporate passive or active cooling, reducing the thermal noise. Amateur astrophotographers using cameras that do not have an internal cooling mechanism have reduced noise by wrapping a plastic bag containing ice around their cameras.
Cooling for reduction of thermal noise is also used in electronic circuitry and equipment including high-end audio and radar instrumentation. In preconditioning a signal for display in an oscilloscope, cooling can be considered as an option for eliminating noise in the interest of boosting vertical resolution. At a minimum, the investigator should be aware of ambient temperature issues. Additionally, crosstalk and electromagnetic interference — for example, coming from a nearby fluorescent ballast or electric motor — sometimes must be considered.
These strategies are implemented outside of (upstream from) the instrument. By eliminating noise they increase vertical resolution. Makers of today’s amazing oscilloscopes have incorporated internal circuitry that further enhances the ability to display signals that are sometimes faint or fleeting. To see how this works, we must consider the relationship between Johnson-Nyquist noise and bandwidth.
In any device such as a resistor there is net current associated with Johnson-Nyquist noise, and accompanying it a voltage that is measurable at the terminals. Of course, the product of the voltage and current is power, which is the key metric.
At 300°K, which may be taken as room temperature, the high-frequency cutoff point is about 50 GHz. This is because above this high frequency the brief time scale does not permit electron fluctuations to occur. There is also a low-frequency cutoff because power is a function of frequency. The instrument’s maximum bandwidth capacity is usually less than determined by the theoretical bandwidth inherent in Johnson-Nyquist noise.
The power of the noise that is injected into the system is proportional to the temperature of the device or conductor and the bandwidth of the system under investigation. From this relationship it follows that reducing the bandwidth also reduces noise. This is a viable maneuver only when the frequency of the signal is not so high as to be eliminated along with the noise.
Most of today’s amazing oscilloscopes have internal means for reducing the bandwidth, and this is a simple way to reduce the amount of noise that could obscure the signal under investigation. Tektronix, for example, introduced bandwidth limiting several years ago. In looking at a noisy signal, if the bandwidth is not intentionally lowered, the instrument will be prone to trigger on multiple rising edges. The result is a display that has fuzzy waveforms and unwanted ghost traces, as the instrument triggers on both true and false rising edges.
Another way to improve vertical resolution is to make use of repetitive waveform averaging. In this maneuver, two or more data acquisitions are averaged on a point-by-point basis. This averaging will reduce the amount of noise to give a cleaner and more authentic representation of the signal on the display. Averaging still more data acquisitions further reduces the noise. The sample size can be increased until the amount of noise no longer compromises the signal as displayed.
To take advantage of this averaging capability in a Tektronix instrument, press acquire. In the acquisition menu, select mode, then average. A sample size can be set to reduce the noise component as desired.
Transient waveform averaging, alternately called high-resolution mode, calculates and displays the average of all values in each sample interval while running at the digitizer’s high sample rate. The vertical resolution is thereby dramatically enhanced.
To get a good look at the amount of noise in a signal as displayed, reduce the oscilloscope’s sample rate. Then zoom in and select single acquisition. Noise is indicated by a jagged appearance of the trace, which is most pronounced at the peaks. The solution is to select acquire, mode, high resolution, and single acquisition. The result becomes apparent — an improved waveform without the irregularities characteristic of noise.
Making use of the internal digital low-pass filter is another strategy that enables the user to suppress noise and thereby get more vertical resolution. The operating mode here is to reduce the sample rate. To do this, shorten the record length.
Select acquire, then record length. By choosing single acquisition, the display will freeze and noise will be quite visible. Use this method to examine a waveform to evaluate the effectiveness of any noise reduction program.
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