Rhode & Schwarz RTC1002 Oscilloscope

The Rhode & Schwarz RTC1002 is a 2-channel oscilloscope with a built in waveform generator. It has a maximum sampling rate of 2Gs/sec.

The Web interface 129.27.158.75 will let you save screen shots of the oscilloscope display, send SCPI commands to the instrument, and download the data that is displayed on channel 1 or channel 2.
R&S RTC1000 Digital Oscilloscope User Manual
R&S HMO1002 Series Digital Oscilloscope SCPI Programmers Manual

Current-voltage characteristics

There is a simple component tester that will plot the current-voltage characteristics of a device like a diode or a resistor. Press the button to bring up a list of utilites and then select COMP. TEST with a soft button.

Attach a cable that has a BNC connector on one end and two aligator clips on the other end to the Aux Out port. Clip the device to be tested on the other end of the cable.

The component test function.

If you want to record the data of a current-voltage characteristic, you will need a transimpedance amplifier such as Femto DLPCA-200 to convert the current to a voltage bacause the oscilloscope can only read a voltage. To use the internal function generator, connect the Aux Out port to Channel 1 and then continue with a BNC cable to apply the voltage from the Aux Out across the device to be tested. Connect the center conductor of the BNC cable to one side of the device to be tested. Connect the other side of the device to be tested to the center conductor of the BNC cable that is connected to the input of the transimpedance amplifier. Connect the two outer conductors of these BNC cables together. Connect the output of the transimpedance amplifier to Channel 2.

Press and select the function generator.
Choose the Function soft button and use the 'Select' knob to choose 'Sinusoid'.
Choose the Frequency soft button and use the 'Select' knob to set a low value such as 11 Hz. Avoid frequencies such as 5 Hz or 10 Hz that have a simple rational relation to 50 Hz.
Choose the Amplitude soft button and use the 'Select' knob the amplitude of the voltage signal.
Choose the Offset soft button and use the 'Select' knob the offset of the voltage signal. For a resistor, an offset of zero is suitable. For a silicon diode, an offset of -1.5 V is suitable and for a light emitting diode an offset of -1.5 V is suitable.
Adjust the horizontal scale to show a few wavelengths and adjust the vertical scale of channel 1 and channel 2 separately. You may have to change the gain on the transimpedance amplifier.
Check that the overload light does not light up on the transimpedance amplifier. If the light is on, adjust the amplitude of the function generator to a smaller value or go to a smaller amplification on the transimpedance amplifier.
Press the button, go to the second page and choose X-Y mode. Press the CH1 button.

X-Y mode

If you are happy with the current-voltage characteristic, run the following program to record the data.

import matplotlib.pyplot as plt
import pyvisa as visa
import numpy as np
#from time import time, sleep
import datetime
import csv

rm = visa.ResourceManager()
        
rso = rm.open_resource('TCPIP::129.27.158.75::INSTR')

rso.write('FORMat ASC,0')

# This program assumes that a transimpedance amplifier is being used to measure the current
gain = 1E5 # V/A

data1 = rso.query('CHANnel1:DATA?')
string_list = data1.split(',')
numerical_list = [float(s.strip()) for s in string_list if s.strip()]
data1_np = np.array(numerical_list)

data2 = rso.query('CHANnel2:DATA?')
string_list = data2.split(',')
numerical_list = [float(s.strip()) for s in string_list if s.strip()]
data2_np = np.array(numerical_list)

I = data2_np*(1/gain)

header1 = rso.query('CHANnel1:DATA:HEADer?')
print('channel1: start time, stop time, number of points, measurements per point: '+header1)
header1_list = header1.split(',')
header1_numerical = [float(s.strip()) for s in header1_list if s.strip()]
start_time=header1_numerical[0]
stop_time=header1_numerical[1]
points=int(header1_numerical[2])
timeaxis = np.linspace(start_time,stop_time, num=points)

rso.close()
        
rm.close()

""" ******* For saving the data ******** """

#some suggestions for improvement of the data saving
    #the file name should identify the file uniquely
    #therefore specifying for example the voltage range, and the
    #type of characteristic (U/I, U/R, etc...) is suggested

# Create unique filenames for saving the data
time_for_name = datetime.datetime.now().strftime("%Y_%m_%d_%H%M%S")
filename_csv = 'RTC1002_' + time_for_name +'.csv'
filename_pdf = 'RTC1002_' + time_for_name +'.pdf'

#initializing a CSV file, to which the measurement data will be written - if this script is used to measure anothcharacteristic than the U/I curve, this has to be changed
# Header for csv
with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow(["time /s,"," Channel 1 / V", "Channel 2 / V"])
        
for nr in range(points):
    with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow([timeaxis[nr],data1_np[nr], data2_np[nr]])
        
""" ******* For plotting the data ******** """

plt.plot(timeaxis,data2_np)
plt.plot(timeaxis,data1_np)
plt.xlabel('time / s', fontsize=14)
plt.ylabel('V', fontsize=14)
plt.title('Channel 1', fontsize=14)
plt.tick_params(labelsize = 14)
plt.show()

fig, ax1 = plt.subplots()

color = 'tab:orange'
ax1.set_xlabel('time [s]')
ax1.set_ylabel('Channel 1 [V]', color=color)
ax1.plot(timeaxis, data1_np, color=color)
ax1.tick_params(axis='y', labelcolor=color)

ax2 = ax1.twinx()  # instantiate a second Axes that shares the same x-axis
color = 'tab:blue'
ax2.set_ylabel('Channel 2 [V]', color=color)
ax2.plot(timeaxis, data2_np, color=color)
ax2.tick_params(axis='y', labelcolor=color)

fig.tight_layout()  # otherwise the right y-label is slightly clipped
plt.show()

Current-voltage characteristics of a diode.

Capacitance/impedance measurements

The frequency dependent impedance of a device is $Z(\omega ) = V(\omega )/I(\omega )$ where $V(\omega )$ is the amplitude of an sinusoidal voltage signal at angular frequency $\omega$ across the device and $I(\omega )$ is the amplitude of resulting sinusoidal current signal passing through the device. If we assume a harmonic form for the voltage, $V = V_0e^{i\omega t}$, then for a resistor,

$$V = IR,$$

and the current is $I = V/R$.

For a capacitor,

$$Q=CV,$$

and the current is,

$$I= \frac{dQ}{dt}= C\frac{dV}{dt} = i\omega CV_0 e^{i\omega t} = \omega CV_0 e^{i(\omega t + \pi/2)}.$$

This means that the current leads the voltage by 90 degrees.

For an inductor,

$$V = L\frac{dI}{dt},$$

and the current is,

$$I= \frac{V_0 e^{i\omega t}}{i\omega L}= \frac{V_0 e^{(i\omega t - \pi/2)}}{ \omega L}.$$

This means that the current lags the voltage by 90 degrees.

A circuit involving multiple resistors, capacitors, and inductors can display a resonance, and generally, the phase will be a function of the frequency.

It is instructive to first measure a capacitor with a known value of capacitance. Connect the BNC cables the same way as for the current-voltage measurement. Connect the Aux Out port to Channel 1 with a BNC cable, and then continue with another BNC cable and connect the center conductor of the BNC cable to one side of the device to be tested. Connect the other side of the device to be tested to the center conductor of the BNC cable that is connected to the input of the transimpedance amplifier. Connect the two outer conductors of these BNC cables together. Connect the output of the transimpedance amplifier to Channel 2.

Press and select the function generator.
Choose the Function soft button and use the 'Select' knob to choose 'Sinusoid'.
Choose the Frequency soft button and use the 'Select' knob to set the frequency to about 10 kHz.
Choose the Amplitude soft button and use the 'Select' knob to set the amplitude in the range 0.1 V - 1 V.
Choose the Offset soft button and use the 'Select' knob to set the offset to zero.
Use the Ch1 button to select AC coupling for channel 1.
Use the Ch2 button to select AC coupling for channel 2.
Set the scope to trigger on the positive slope of channel 1.

If the scope is triggering on the positive slope of the voltage signal at a level of 0 V, the current should have a maximum at the center of the screen. The oscilloscope screen should look something like this:

CH1 (yellow) is the voltage output by the function generator.
CH2 (blue) is the voltage output of the transimpedance amplifier.

Change the frequency of the function generator and notice that the amplitude of the current changes, $|I|= \omega CV_0$. We could try to read the amplitude and the phase of the current from the oscilloscope screen, but it is better to project both signals onto sine and cosine functions.

$$V_1(t) = a_{s1}\sin(2\pi ft) + a_{c1}\cos(2\pi ft),$$ $$V_2(t) = a_{s2} \sin(2\pi ft) + a_{c2}\cos(2\pi ft).$$

Multiply $V_1(t) by $\sin(2\pi ft)$ and integrate over an integer number of periods.

$$\int_0^T V_1(t)\sin(2\pi ft) dt= \int_0^T a_{s1} \sin^2(2\pi ft)dt = \frac{a_{s1}T}{2}$$

In a similar manner, you can show that,

$$a_{s1} = \frac{2}{T}\int_0^T V_1(t)\sin(2\pi ft) dt,$$ $$a_{c1} = \frac{2}{T}\int_0^T V_1(t)\cos(2\pi ft) dt,$$ $$a_{s2} = \frac{2}{T}\int_0^T V_2(t)\sin(2\pi ft) dt,$$ $$a_{c2} = \frac{2}{T}\int_0^T V_2(t)\cos(2\pi ft) dt.$$

The amplitude of $V_1$ is $A_1 = \sqrt{a_{s1}^2 + a_{c1}^2}$ and the phase is $\phi_1 = \text{atan} (a_{c1}/a_{s1})$. There are similar expressions for $V_2$. The impedance is,

$$Z = \frac{A_1g}{A_2} e^{i(\phi_1-\phi_2)}, $$

where $g$ is the gain of the transimpedance amplifier. If we assume that we are measuring a capacitor, the capacitance is,

$$C = \frac{1}{2\pi f |Z|}$$

and the phase shift should be 90°.

The following code calculates the impedance of a device as a function of frequency. After you have found suitable amplitude and frequency ranges for the current and voltage signals, set the total time interval displayed on the screen of the oscilloscope to be a few periods of the lowest frequency that will be measured and run the program.

import matplotlib.pyplot as plt
import pyvisa as visa
import numpy as np
from time import sleep
import datetime
import csv
import math

rm = visa.ResourceManager()
        
rso = rm.open_resource('TCPIP::129.27.158.75::INSTR')

rso.write('FORMat ASC,0')

sine = np.empty(points)
cosine = np.empty(points)
Z = []
phi = []
C = []
gain = 1E4 # V/A
freq = []
f0 = 1000
nf = 30

for x in range(nf):
    f = 500*x + f0 # frequency
    rso.write('GENerator:FREQuency '+str(f))
    
    for nr in range(points):
        sine[nr]=math.sin(2*math.pi*f*timeaxis[nr])
        cosine[nr]=math.cos(2*math.pi*f*timeaxis[nr])

sleep(2) # wait for the oscilloscope to settle
    
    data1 = rso.query('CHANnel1:DATA?')
    string_list = data1.split(',')
    numerical_list = [float(s.strip()) for s in string_list if s.strip()]
    data1_np = np.array(numerical_list)

data2 = rso.query('CHANnel2:DATA?')
    string_list = data2.split(',')
    numerical_list = [float(s.strip()) for s in string_list if s.strip()]
    data2_np = np.array(numerical_list)

in_phase1 = sine*data1_np
    out_phase1 = cosine*data1_np
    as1 = 2*np.trapz(in_phase1,timeaxis)/(stop_time-start_time)
    ac1 = 2*np.trapz(out_phase1,timeaxis)/(stop_time-start_time)
    amp1 = math.sqrt(as1*as1 + ac1*ac1)
    phase1 = math.atan2(ac1,as1)

in_phase2 = sine*data2_np
    out_phase2 = cosine*data2_np
    as2 = 2*np.trapz(in_phase2,timeaxis)/(stop_time-start_time)
    ac2 = 2*np.trapz(out_phase2,timeaxis)/(stop_time-start_time)
    amp2 = math.sqrt(as2*as2 + ac2*ac2)
    phase2 = math.atan2(ac2,as2)
    
    Zi = amp1*gain/amp2
    Z.append(Zi)
    phi.append((phase1 - phase2)*180/math.pi)
    freq.append(f)
    C.append(1/(2*math.pi*f*Zi))

rso.close()   
rm.close()

print('The capacitance values are')
for x in range(nf):
    f = 500*x + f0
    print('frequency: '+str(f)+'  capacitance: '+str(C[x]))

""" ******* For saving the data ******** """

# Create unique filenames for saving the data
time_for_name = datetime.datetime.now().strftime("%Y_%m_%d_%H%M%S")
filename_csv = 'impedance_' + time_for_name +'.csv'
filename_pdf = 'impedance_' + time_for_name +'.pdf'

#initializing a CSV file, to which the measurement data will be written - if this script is used to measure anothcharacteristic than the U/I curve, this has to be changed
# Header for csv
with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow(["frequency,","Z", "phase"])
        
for nr in range(nf):
    with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow([freq[nr],Z[nr], phi[nr]])
        
""" ******* For plotting the data ******** """

fig, ax1 = plt.subplots()

color = 'tab:red'
ax1.set_xlabel('frequency')
ax1.set_ylabel('Z', color=color)
ax1.plot(freq, Z, color=color)
ax1.tick_params(axis='y', labelcolor=color)

ax2 = ax1.twinx()  # instantiate a second Axes that shares the same x-axis
color = 'tab:blue'
ax2.set_ylabel('phase', color=color)
ax2.plot(freq, phi, color=color)
ax2.tick_params(axis='y', labelcolor=color)

fig.tight_layout()  # otherwise the right y-label is slightly clipped
plt.show()

The program prints the capacitance values in the python output panel and generates a plot such as the one shown below.

For this measurement, a capacitor that was nominally 10 nF was used, and the $1/f$ frequency dependence that is expected is observed, but the phase shifts away from 90°. This is a typical feature of a transimpedance amplifier.

To measure the capacitance of a diode, press and select the function generator. Choose the Offset soft button and use the 'Select' knob to set the offset to reverse bias the diode. Be sure the amplitude of the ac signal is small enough that the diode is always reverse-biased. Use ac coupling for both channels and ac coupling on the tran simpedance amplifier.

Capacitance - Voltage measurements

Capacitance - voltage measurements can provide information about the doping concentrations in a diode or a MOSFET. The measurement can be performed either with the internal function generator of the oscilloscope or an external function generator. The code below uses a Keithley Model 3390 Arbitrary Waveform Generator.

For diodes, first find the ranges of amplitudes and frequencies that make a good capacitance measurement using the program above. The capacitance value should stay constant over a range of frequencies. Choose a frequency in the middle of the good range to perform the CV measurement.

Connect the output of the Keithley 3390 to Channel 1 with a BNC cable and then continue with another BNC cable, and connect the center conductor of the BNC cable to one side of the device to be tested. Connect the other side of the device to be tested to the center conductor of the BNC cable that is connected to the input of the transimpedance amplifier. Connect the two outer conductors of these BNC cables together. Connect the output of the transimpedance amplifier to Channel 2. On the Keithley 3390, select a sinusoidal waveform and a suitable frequency. The amplitude should be 0.1 V or less so that the ac signal does not modulate the depletion region too much. Change the offset voltage, 'Vos', and you should see the capacitance change for different reverse bias voltages. Set the time scale of the oscilloscope to show about 20 periods of the oscillation. The following program will change the bias voltage and measure the capacitance at each bias voltage.

import matplotlib.pyplot as plt
import pyvisa as visa
import numpy as np
from time import sleep
import datetime
import csv
import math

rm = visa.ResourceManager()
        
rso = rm.open_resource('TCPIP::129.27.158.75::INSTR')

Keithley_3390 = rm.open_resource('USB::0x05E6::0x3390::1421720::INSTR')

# set up the function generator
Keithley_3390.write('OUTPut OFF')         # disable output
Keithley_3390.write('FUNCtion SINusoid') # Function types :{SINusoid | SQUare | RAMP | PULSe | NOISe | DC | USER }
Keithley_3390.write('FREQuency 10 kHz')   # frequency {uHz | mHz | Hz | kHz | MHz}    1uHz < f < 50 MHz
Keithley_3390.write('VOLTage:UNIT Vpp')  # {Vpp | Vrms | dBm}
Keithley_3390.write('VOLTage 100 mV')       # mV or V

Keithley_3390.write('OUTPut ON')         # enable output

rso.write('FORMat ASC,0')

sine = np.empty(points)
cosine = np.empty(points)
Z = []
phi = []
C = []
gain = 1E7 # V/A
V = []
f = 10000
VR = np.linspace(-4.8,0, num=30)

for nr in range(points):
    sine[nr]=math.sin(2*math.pi*f*timeaxis[nr])
    cosine[nr]=math.cos(2*math.pi*f*timeaxis[nr])

for x in VR:
    Keithley_3390.write('VOLTage:OFFSet '+str(x)+' V')  # mV or V

sleep(3) # wait for the oscilloscope to settle
    
    data1 = rso.query('CHANnel1:DATA?')
    string_list = data1.split(',')
    numerical_list = [float(s.strip()) for s in string_list if s.strip()]
    data1_np = np.array(numerical_list)

data2 = rso.query('CHANnel2:DATA?')
    string_list = data2.split(',')
    numerical_list = [float(s.strip()) for s in string_list if s.strip()]
    data2_np = np.array(numerical_list)

""" ******* For saving the data ******** """

# Create unique filenames for saving the data
time_for_name = datetime.datetime.now().strftime("%Y_%m_%d_%H%M%S")
filename_csv = 'cv_' + time_for_name +'.csv'
filename_pdf = 'cv_' + time_for_name +'.pdf'

#initializing a CSV file, to which the measurement data will be written - if this script is used to measure anothcharacteristic than the U/I curve, this has to be changed
# Header for csv
with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow(["V,","C"])
        
for nr in range(30):
    with open(filename_csv, 'a') as csvfile:
        writer = csv.writer(csvfile, delimiter=';',  lineterminator='\n')
        writer.writerow([VR[nr],C[nr]])

""" ******* For plotting the data ******** """

plt.plot(VR,C)
plt.xlabel('V', fontsize=14)
plt.ylabel('C', fontsize=14)
plt.tick_params(labelsize = 14)
plt.show()

The plot below shows the capacitance-voltage characteristic of a light emitting diode. See: Capacitance - Voltage properties of a pn junction .

The capacitance-voltage characteristics of a MOSFET were measured by shorting the source and drain together. See: MOS Capacitor - Capacitance voltage characteristics.







Semiconductor Laboratory