**General Description**

High impedance (Hi-Z) probes are the most commonly used oscilloscope probes. They are available with attenuation factors of 10:1 (X10) and 100:1 (X100) and bandwidths of up to 350 MHz. However, it is important to point out that while the bandwidth may be as high as 350 MHz, in practice high impedance probes are typically used in applications where the signal frequency is below 50 MHz. The poor high frequency performance of these probes is due largely to the adverse effects of capacitance loading. Consider the typical X10 probe shown schematically in figure 3.

The impedance input of a typical 300 MHz bandwidth oscilloscope consists of a 1 MOhm resistance in parallel with a 15 pF capacitor. Direct connection of the oscilloscope to a circuit by means of a coaxial cable or X1 probe will add an additional capacitive load, due to the cable, of approximately 50 pF per meter. The combination of the input and cable capacitance is approximately 65 pF. The oscilloscope input impedance is represented in the probe schematic by R2 and C2. Both the oscilloscope and cable capacitances are represented by C2. The high impedance probe isolates the measured circuit by adding a large resistor, R1 in this example, in series with the oscilloscope input. R1 forms a resistive voltage divider with the oscilloscope input resistance, R2. The value of R1 is set to 9 MOhm for a X10 probe and 99 MOhm for a X100 probe for an oscilloscope input resistance of 1 MOhm. Capacitor C1 is adjusted so that the RC product, R1C1, equals the product R2C2. This compensates the probe so that it provides the desired attenuation at all frequencies. Therefore, before using any high impedance passive probe, the user should adjust C1 with a 1 kHz square wave, to seek an optimal compensation. A typical X10 probe has an equivalent input impedance consisting of a 10 M resistance in parallel with 15 pF, where the 15 pF are partly due to the series of C1 and C2 and partly to the stray capacitance of the probe tip to ground, Ctip.

As previously mentioned, the high impedance probe is best suited for general purpose applications where the signal frequencies are below 50 MHz. These probes are relatively inexpensive and, since they use only passive components, they are mechanically and electrically rugged. In addition, they have a very wide dynamic range. The low end of the amplitude range is limited by the probe attenuation factor and the vertical sensitivity of the oscilloscope. The attenuation does, however, offer advantages in dealing with high level signals up to the maximum input voltage range, typically 600 Volts for 10:1 probes. Mechanically, these probes are available with a variety of convenient cable lengths and are generally supplied with a wide variety of probe tips, adaptors, and ground leads.

**How High Impedance Probes Affect Measurements**

When an oscilloscope is used to make measurements in a circuit or device, it is advantageous to anticipate how the device being measured is affected by the instrument. In most cases, it is possible to model the oscilloscope's input circuits, including the probes, and to quantify the loading effects and signal aberrations. The user's knowledge of the measured circuit, together with the oscilloscope manufacturer's characterization of the oscilloscope/probe specifications, can be combined to model the entire measurement system.

Consider the simplified measurement system model shown in figure 4. The actual circuits of the oscilloscope and of the high impedance probe have been reduced to an equivalent parallel resistorcapacitor (RC) circuit. Similarly, as was done in a previous discussion, the circuit being measured has been simplified and reduced to its Thevenin equivalent form. If the circuit's source resistance, Rs, is approximately 50Ohms and the measurement is made using a conventional 10:1 high impedance probe, then it is reasonable to ignore the probe's 10 MOhm resistance, Ro. The equivalent circuit for the system now consists of a series resistance, Rs, and a shunt capacitance, with a value equal to the sum of the source, Cs, and the input capacitance of the probe/oscilloscope, Co. From this simple model we can predict the effect of the oscilloscope on the risetime of the circuit. Using classical circuit analysis, the risetime, tr, of this RC circuit in response to a step function input is related to the values of resistance and capacitance by the equation:

$$ tt = 2.2RC $$

The following example, using typical component values, will provide good insight into the effects of using a high impedance probe:

$$ For: Rs = 50 Ohms, \space Cs = 9 pF, \space and \space Co = 15 pF $$

The risetime of the source alone, trs, is:

$$ trs = 2.2 (50) (9 10 -12) = 1 ns $$

The risetime of the source with the probe and oscilloscope connected, tros, is:

$$ tros = 2.2 (50) (24 10 -12) = 2.6 ns $$

The act of connecting the probe increased the risetime by 160% due to the additional capacitance of the probe.

The additional capacitance also increases the loading on the generator, especially at higher frequencies. The capacitive reactance component of the load impedance varies inversely with frequency as described in the following equation:

$$ x^0 = {1 \over {2πfC}} $$

where the capacitive reactance, Xc, in Ohms, is an inverse function of frequency, f, in Hertz, and capacitance, C, in Farads. A simple calculation using the values from our previous example will show this increased loading. At a frequency of 100 MHz, the load impedance due to the total capacitance of 24 pF is:

$$ X_1 = {1 \over {2π(100x10^6)(24x10^{-12})}} = {66 Ω} $$

Obviously, at frequencies above several kilohertz the capacitive loading becomes the major element loading the source. The 10 MOhm input resistance of the high impedance probe only applies at DC. On the basis of these two examples it should be obvious why so much effort is put into lowering the input capacitance of oscilloscope probes. Obviously, at frequencies above several kilohertz the capacitive loading becomes the major element loading the source. The 10 MOhm input resistance of the high impedance probe only applies at DC. On the basis of these two examples it should be obvious why so much effort is put into lowering the input capacitance of oscilloscope probes.

Another approach to characterize the effects of connecting a probe to a circuit is to consider how it affects the bandwidth of the circuit. The bandwidth of this RC circuit, actually a simple low pass filter, is the frequency at which the output voltage falls to 0.707 of the unloaded source voltage.

The following relationship is used to calculate the bandwidth, BW, in Hz, of this RC circuit, for resistance in Ohms and capacitance in Farads:

$$ BW = {1 \over {2πRC}} $$

There is another classic equation which relates the risetime, tr, in seconds, and bandwidth, BW, in Hertz, of this simple RC circuit model:

$$ t_s = {0.35 \over BW} $$

The last equation is useful because many oscilloscope and probe specifications are described in terms of bandwidth and not risetime.

A knowledge of the risetime of each stage in a multistage, cascaded measurement can be used to estimate the composite risetime. The risetime of the composite system is the quadratic sum, i.e. the square root of the sum of the squares of the risetime of each element. For instance, the risetime of a signal shown on an oscilloscope screen, the measured risetime, includes the actual signal risetime as well as the risetime of the measurement system. It is possible, using the following relationship, to calculate the actual risetime of the signal, tsig, based on the measured risetime, tmeas, and a knowledge of the system risetime, tsys:

$$ t_{sig} = {\sqrt{t^2_{meas} - t^2_{sys}}} $$

To see how these equations can be used, consider the following practical example:

A pulse risetime measurement is made with an oscilloscope using a 10:1 probe which has a bandwidth at "the probe tip" of >250 MHz. The goal is to estimate the actual risetime of the signal. The oscilloscope's parameter readout provides the measured value, as shown in figure 5. The oscilloscope manufacturer's specification provides a composite risetime for both the oscilloscope and the probe (assuming a 25 source impedance), combining both into a single value. The signal risetime can be estimated as follows:

$$ t_{means} = 1.69ns $$ $$ t_{sys} = {0.35 \over {250*10^6}} = 1.4ns $$ $$ t_{sys} = {\sqrt{t^2_{meas} - t^2_{sys}}} = {\sqrt{(1.69*10^{-9})^2}} $$

Since the bandwidth of the oscilloscope and probe combination was only specified as a limiting value, i.e. >250 MHz, the calculated value is a lower limit. If a signal with known risetime and source impedance is measured, then it is possible using the same relation-ship, to determine the bandwidth of the oscilloscope "at the probe tip".

The dynamic performance of the high impedance probe is easily determined using the preceding equations. Keep in mind that these equations provide the first order estimation of a probe's behavior. In the last chapter, second order effects such as stray inductance in ground leads, will be discussed.