Oscilloscopes I: triggering, timebase and probes

A multimeter gives one number. An oscilloscope shows how a voltage changes with time, and that picture reveals things no meter can: the shape of a ripple waveform, the ringing on a logic edge, the delay between a button press and a response, a glitch that happens once in a thousand cycles. Almost every modern bench scope is a digital storage oscilloscope, which samples the input with a fast analog-to-digital converter, stores the samples in memory and draws them on a screen. This lesson covers the controls you use every time: vertical scale and coupling, the timebase, triggering, the automatic measurements and the passive probe, including the compensation step that many people skip.

Amara asks Leo to look at three signals on the controller board: the 24 V rail's ripple, the 5 V logic clock driving the shift registers that select the signal heads, and the output of the push-button debouncer when the button is pressed. Each one needs a different setup, and each one teaches a control.

The display and the vertical controls

The screen is a grid, usually ten divisions across and eight divisions high. The vertical scale, in volts per division, sets how many volts each division represents, and the position control moves the trace up or down. The input coupling selects what reaches the converter: DC coupling passes the whole signal, including its DC level; AC coupling inserts a series capacitor that blocks DC and passes only the changing part, with a low-frequency corner of a few hertz; and ground disconnects the input to show where zero is. To see 200 mV of ripple riding on a 24 V rail, DC coupling at 50 mV per division would put the trace far off the screen. AC coupling removes the 24 V and lets you expand the ripple to fill the screen.

Because the converter has a fixed number of bits, usually 8 on a general-purpose scope and 10 to 12 on high-resolution ones, the vertical scale sets the resolution too. An 8-bit converter spread over eight divisions has 256 levels, so at 1 V per division each level is about 31 mV. Small details on a large signal disappear into the quantization. Adjust the vertical scale so the signal fills most of the screen; this uses the converter's full range and gives the most precise measurements.

The timebase and acquisition memory

The horizontal scale, in seconds per division, sets the time window: at 1 ms per division, ten divisions show 10 ms. The horizontal position control moves the window relative to the trigger point. Behind the scenes, the scope has a maximum sample rate, for example 1 GSa/s, and a memory depth, the number of samples it can store per acquisition, for example 10 Mpoints. The sample rate actually used is the memory depth divided by the time window, up to the maximum. Over a long window, a scope with shallow memory has to reduce its sample rate, and fast details can be lost or aliased, a problem lesson 7 returns to. Deep memory lets you capture a long window and still zoom in on fast events.

Triggering: making the picture stand still

A repeating waveform only looks stable on screen if every sweep starts at the same point in its cycle. The trigger decides that point. The simplest and most used is the edge trigger: start the sweep when the signal crosses a set level in a set direction, rising or falling. Set the level in the middle of the waveform, choose the slope, and a repeating signal locks in place. If the level is above the waveform's peak or below its trough, no trigger occurs, and the scope either waits forever or free-runs and shows a smeared mess, depending on the trigger mode.

Single mode is the one beginners forget, and it is the one that captures the most informative events. A button press, a power-up surge, a fault that happens once a minute: none of them repeat in a way that auto or normal mode can hold. Set the trigger level and slope where the event should cross, press Single, then cause the event. The scope captures it, stops, and keeps it on screen for measurement. Because the trigger point is in the middle of the record by default, you also see what led up to it. Beyond edge triggers, modern scopes offer pulse-width triggers, which fire on a pulse shorter or longer than a set time and catch glitches; runt triggers, which fire on a pulse that crosses one level but not another; and serial-bus triggers that decode protocols such as I²C, SPI and UART and trigger on a particular message.

Automatic measurements and cursors

Digital scopes measure waveforms automatically: frequency, period, peak-to-peak and RMS amplitude, mean, rise and fall time, pulse width, duty cycle, overshoot and the delay between channels. These are quick and usually more precise than reading the grid by eye, but they compute what they are told on whatever is on screen. A frequency measurement on a noisy signal with only part of a cycle on screen will be wrong; an RMS measurement over a window that does not contain a whole number of cycles will be slightly off. Rise time is conventionally measured between the 10 % and 90 % points of the transition, so the scope needs a clean top and bottom level to find them. Cursors, adjustable lines you place on the screen, let you measure any two points by hand and are useful when the automatic measurement is confused.

The passive probe

The standard probe supplied with a scope is a 10:1 (10X) passive probe. The scope input is about 1 MΩ in parallel with 10 to 20 pF, and the probe puts a 9 MΩ resistor in its tip so that, together with the scope's 1 MΩ, the signal is divided by ten and the circuit sees 10 MΩ instead of 1 MΩ. The cable and scope input add capacitance, which would turn that 9 MΩ into a low-pass filter. The probe therefore includes an adjustable compensation capacitor that makes the divider's time constants equal at the tip and at the scope end, so the division ratio is ten at every frequency. Seen from the circuit, a 10X probe looks like 10 MΩ in parallel with roughly 10 to 15 pF.

A 1X probe, or a probe switched to 1X, connects the circuit straight to the scope input through the cable. It gives full sensitivity, which helps with millivolt signals, but presents about 1 MΩ and the full cable and input capacitance, often 50 pF or more, and its bandwidth is typically only a few megahertz. For almost all general work, use 10X, and check that the scope's channel setting matches the probe so the displayed volts are right. Many probes identify themselves to the scope automatically; others need the attenuation set in the channel menu.

Compensating the probe

Every time a probe is connected to a different scope input, its compensation should be checked. Each scope has a calibration output on the front panel, a square wave of about 1 kHz and a few volts. Connect the probe to it, display a few cycles, and adjust the small screw on the probe until the square wave has flat tops. An undercompensated probe rounds the corners, attenuating high frequencies; an overcompensated probe shows peaks on the leading edges, boosting them. Either error changes rise-time measurements and the apparent amplitude of fast signals by many percent.

# Probe compensation: response of a 10X divider with mismatched capacitors to a step
import math
Rtip, Rin = 9e6, 1e6
Cin = 20e-12 + 80e-12          # scope input plus cable
Cc_correct = Rin * Cin / Rtip   # tip capacitor that balances the divider
print(f"Correct tip capacitance: {Cc_correct*1e12:.2f} pF")

def step_response(Ctip, t):
    # Divider of two RC sections: initial value set by capacitors, final by resistors
    v0 = Ctip / (Ctip + Cin)            # high-frequency ratio (capacitive divider)
    vinf = Rin / (Rin + Rtip)           # low-frequency ratio (resistive divider)
    tau = (Rtip * Rin / (Rtip + Rin)) * (Ctip + Cin)
    return vinf + (v0 - vinf) * math.exp(-t / tau), tau

for label, c in (("under", 0.7 * Cc_correct), ("correct", Cc_correct), ("over", 1.3 * Cc_correct)):
    v0, tau = step_response(c, 0.0)
    v_late, _ = step_response(c, 5 * tau)
    print(f"{label:8s} Ctip = {c*1e12:5.2f} pF: edge starts at {10*v0:.3f}, settles to {10*v_late:.3f} "
          f"(tau = {tau*1e6:.1f} us)")

Correct tip capacitance: 11.11 pF
under    Ctip =  7.78 pF: edge starts at 0.722, settles to 0.998 (tau = 97.0 us)
correct  Ctip = 11.11 pF: edge starts at 1.000, settles to 1.000 (tau = 100.0 us)
over     Ctip = 14.44 pF: edge starts at 1.262, settles to 1.002 (tau = 103.0 us)

The program shows the physics behind the three pictures. At the instant of a step, the divider ratio is set by the capacitors; long after, by the resistors. When the capacitive ratio is too small, the edge starts low and creeps up; when it is too large, the edge starts high and decays. Only when R_tip·C_tip equals R_in·C_in do the two ratios match, and the edge is a clean step. The settling time constant, around a hundred microseconds, is why the error is easy to see on a 1 kHz calibration square wave.

The ground lead

The probe's ground lead, the short wire with an alligator clip, connects the probe's shield to the circuit's ground. It is part of the measurement loop, and its inductance, roughly 1 nH per millimetre, forms a resonant circuit with the probe's input capacitance. On slow signals that does not matter. On fast edges, a 15 cm ground lead can add ringing at a few hundred megahertz that is not in the circuit at all. For fast signals, replace the long lead with the short spring ground tip that comes with the probe, and touch it to a ground pad right beside the signal point. Never clip the ground lead to anything that is not at ground potential; lesson 7 explains why on a mains-powered scope.