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 screenshots 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 utilities and then select COMP. TEST with a soft button.

Attach a cable that has a BNC connector on one end and two alligator 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 because 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. Use dc coupling for both channels. 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
import os
import elabapi_python
import eLabFTW_config_api2_semilab as eLab

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 ******** """

# 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 another characteristic 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()

""" ********** saving to elabFTW  ******* """

experiment_title = "RTC IV"
elab_manager = eLab.Helper_elabftw()
experiment_ID = elab_manager.set_experiment(experiment_title)

# prepare to upload this script
filename_scr = __file__

# consider all data files that were generated
elab_manager.upload_file(experiment_ID, filename_csv)
elab_manager.upload_file(experiment_ID, filename_pdf)
elab_manager.upload_file(experiment_ID, filename_scr)

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 resistor and a capacitor with known values. We will use the Keithley Model 3390 Arbitrary Waveform Generator to generate an AC voltage. 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. The oscilloscope should display the the sinusoidal voltage on Channel 1 and the sinusoidal current on Channel 2. For a resistor the current and the voltage should be in phase and for a capacitor, the current and voltage should be out of phase.

When measuring a capacitor while 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. For a resistor we expect that the amplitude stays constant and that the current and voltage are in phase for all frequencies. For a capacitor we expect that the amplitude of the current changes, $|I|= \omega CV_0$, and the voltage leads the current by 90°. 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. We express the voltages on Channel 1 and Channel 2 in terms of sine and cosine.

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

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. For a resistor, $R = Z$ and $\phi_1 - \phi_2 =0$, while for a capacitor, the capacitance is,

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

and the phase shift should be $\phi_1 - \phi_2 =90$.

The plots below show the measured impedance for a 100 kΩ resistor on the left, and a 100 pF capacitor on the right. The resistance measurement is correct in the limit of low frequencies but at higher frequencies both the amplitude of the impedance and the phase are not what is expected. The problem is that gain of the transimpedance amplifier decreases with frequency and the amplifier adds a phase shift to the signal. For measuring resistances, we could restrict ourselves to low frequencies but this is not a suitable solution for capacitances. The current through a capacitor is proportional to frequency so it vanishes at low frequency. Notice also that the impedance is going up for the capacitor at high frequencies when we expect it to go down.


100 kΩ resistor	100 pF capacitor

To compensate for the frequency dependence of the gain and the phase shift, the impedance and the phase shift of the resistor are fit to parabolic functions. The following code will perform this fit. It is necessary to input the time base (TB in the upper-left corner of the oscilloscope) and the gain of the transimpedance amplifier. The program selects frequencies that correspond to an integer number of wavelengths in the recorded time series.

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

#for use of ELABFTW
import os
import elabapi_python
import eLabFTW_config_api2_semilab as eLab

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('VOLTage:OFFSet -2 V')  # mV or V
Keithley_3390.write('OUTPut ON')         # enable output

rso.write('FORMat ASC,0')

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])  # number of data points in the time series
timeaxis = np.linspace(start_time,stop_time, num=points)

sine = np.empty(points)
cosine = np.empty(points)
Z = []
phi = []
phi_fit = []
C = []
freq = []
timebase = 10E-6  # TB from upper-left corner of the oscilloscope
gain = 1E6 # V/A from the transimpedance amplifier
f0 = 1/(12*timebase)
nf = 30  # number of frequencies that are used

for x in range(nf):
    f = x/(12*timebase) + f0 # frequency
    Keithley_3390.write('FREQuency '+str(f)+' Hz')
    
    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)  #integrate sine * V1
    ac1 = 2*np.trapz(out_phase1,timeaxis)/(stop_time-start_time)  #integrate cosine * V1
    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)  #integrate sine * V2
    ac2 = 2*np.trapz(out_phase2,timeaxis)/(stop_time-start_time)  #integrate cosine * V2
    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))  # only relevant when measuring a capacitor

rso.close()   
rm.close()

# fit the phase measurements to a parabola
def fit_phase(x, a,b,c):
    return a*x*x + b*x + c

popt, pcov = curve_fit(fit_phase, freq, phi)

print('Phase fit  a: '+str(popt[0])+'  b: '+str(popt[1])+'  c: '+str(popt[2]))
freqaxis = np.linspace(f0,nf/(timebase*12), num=300)
phi_fit = popt[0]*freqaxis*freqaxis + popt[1]*freqaxis + popt[2]

# fit the impedance measurements to a parabola
def fit_Z(x, a,b,c,d):
    return (a*x*x + b*x + c)/x

popt, pcov = curve_fit(fit_phase, freq, Z)
print('Z fit  a: '+str(popt[0])+'  b: '+str(popt[1])+'  c: '+str(popt[2]))
Z_fit = popt[0]*freqaxis*freqaxis + popt[1]*freqaxis + popt[2]

""" ******* 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.plot(freqaxis, Z_fit, color=color, linestyle='dashed')
ax1.tick_params(axis='y', labelcolor=color)
#ax1.set_yscale('log')

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.plot(freqaxis, phi_fit, color=color, linestyle='dashed')
ax2.tick_params(axis='y', labelcolor=color)

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

# define the title of your experiment, under this name the experiment will be stored in ElabFTW
exp_title = "Impedance fit"

# Connect to eLab

elab_manager = eLab.Helper_elabftw()
experiment_ID = elab_manager.set_experiment(exp_title)
print(experiment_ID)

# Upload files to eLab
#filename_scr = __file__
#elab_manager.upload_file(experiment_ID, filename_csv)
#elab_manager.upload_file(experiment_ID, filename_pdf)
#elab_manager.upload_file(experiment_ID, filename_scr)

The dashed line are fits to the data.

Different fit parameters have to be used for each gain setting of the transimpedance 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')

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)

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)
    C.append(1/(2*math.pi*f*Zi)) # 
    
Keithley_3390.write('OUTPut OFF') 
Keithley_3390.close() 
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 = '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 another characteristic 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