A crocodile clip probe is used to measure a digital signal. The input to the scope is a 1 Meg resistance in parallel with 20 pF. Furthermore, the probe is 0.8 m long and for the co-ax C = 100pF/m. A 10 ns rise time (10% - 90%) pulse is measured. The source impedance for the digital signal output being measured is 60 ohms. At the high frequencies (around the signal bandwidth), what is the typical error made (in relationship to the signal) in the measurements at these high end frequencies? Enter the value of the error in percentage without the %.

To calculate the error made in the measurements at high frequencies, we first need to calculate the total capacitance and the total resistance of the system.

1. Calculate the total capacitance:

The total capacitance (C_total) is the sum of the capacitance of the probe (C_probe) and the capacitance of the scope (C_scope).

C_probe = length of the probe * capacitance per meter = 0.8 m * 100 pF/m = 80 pF

C_scope = 20 pF

So, C_total = C_probe + C_scope = 80 pF + 20 pF = 100 pF

2. Calculate the total resistance:

The total resistance (R_total) is the sum of the resistance of the probe (R_probe) and the resistance of the scope (R_scope).

R_probe = 60 ohms (source impedance for the digital signal output)

R_scope = 1 Meg ohm = 1,000,000 ohms

So, R_total = R_probe + R_scope = 60 ohms + 1,000,000 ohms = 1,000,060 ohms

3. Calculate the time constant (τ):

The time constant of a system is the product of the total resistance and the total capacitance.

τ = R_total * C_total = 1,000,060 ohms * 100 pF = 100 ns

4. Calculate the error:

The error is the difference between the rise time of the pulse and the time constant, divided by the rise time of the pulse, expressed as a percentage.

Error = ((τ - rise time) / rise time) * 100% = ((100 ns - 10 ns) / 10 ns) * 100% = 900%

So, the typical error made in the measurements at these high end frequencies is 900%.