Function generators, amplitude conventions & source impedance
Model a laboratory function generator as a Thévenin source before trusting its amplitude display. Derive Vload=VthZL/(Rs+ZL), explain the common 50 Ω-source / selectable expected-load convention without treating it as universal, convert among Vpp, Vpk, Vrms and dBm with the required waveform/load assumptions, separate DC offset from AC amplitude, and show why a frequency-dependent DUT impedance makes the actual applied Vin change during a sweep.
- Represent a function generator by a Thévenin voltage and finite output impedance before connecting a load.
- Derive the load voltage Vload=Vth ZL/(Rs+ZL) and identify open-circuit and matched-load limits.
- Explain the common 50 Ω output architecture and why a generator’s load setting may change displayed amplitude without changing its physical source resistance.
- Convert sinusoidal Vpp, Vpk and Vrms correctly and keep DC offset as a separate quantity.
- Convert between sinusoidal voltage/power and dBm only when the load resistance is known and the waveform assumptions are stated.
- Predict the factor-of-two amplitude difference between high-impedance and matched loads for an ideal 50 Ω Thévenin source.
- Explain why Vin at the DUT can vary with frequency when the DUT impedance varies, even if the generator setting is unchanged.
- Distinguish low-frequency lumped voltage-divider reasoning from high-frequency transmission-line/mismatch behavior that requires a fuller model.
- Build a source-connection checklist including output reference/ground topology, source impedance, expected load, amplitude unit, offset and DUT impedance.
You set a generator to “1 Vpp” and connect it to a DUT. Is the DUT necessarily receiving 1 Vpp? No: the answer depends on source impedance, load impedance and what the generator means by its displayed amplitude.
The correct starting model is a source with finite output impedance.
04.1Model the generator as a Thévenin source
At frequencies where a lumped model is adequate, represent the generator by an ideal source Vth in series with output impedance Rs or more generally Zs.
For a resistive source/load,
Figure 4.1 — The amplitude setting is not enough: what reaches the load?
The one question is: how do Rs and ZL turn internal source voltage into DUT voltage?
Applied voltage depends on the divider formed by source output impedance and load impedance. A generator display value is meaningful only together with its load convention.
The DUT voltage is therefore a circuit result, not merely a front-panel setting.
04.2The matched-load factor of two
A common laboratory architecture uses Rs=50 Ω. If RL=50 Ω,
If the load is very large compared with 50 Ω,
Thus the same physical source can produce nearly twice the voltage into a high-impedance load as into a matched 50 Ω load.
04.3The load setting often changes the displayed expectation, not the physical source resistor
Many generators let the user select an expected load such as “50 Ω” or “High-Z.” In a common implementation, this setting tells the instrument how to report the voltage expected at that load; the physical series output resistance remains unchanged.
Example: suppose the generator uses a 50 Ω source and displays 1 Vpp into 50 Ω. The internal open-circuit Thévenin amplitude is then 2 Vpp. If a high-impedance oscilloscope input is connected instead of 50 Ω, the observed amplitude will approach 2 Vpp.
This is not a mysterious calibration error. It is the expected divider behavior.
04.4Vpp, Vpk, Vrms and offset describe different quantities
For a zero-centered sine wave
the standard relations are
With a DC offset Voff,
The offset shifts the waveform vertically but does not change Vpp. Peak high/low values are
Generator output limits often constrain the combined amplitude plus offset, so both must be checked.
04.5dBm is power relative to 1 mW, not a voltage unit
For a sine wave delivered to a known resistive load R,
Therefore a dBm value can be converted to voltage only after R is specified.
For example, 0 dBm means 1 mW. Into 50 Ω,
Into another resistance, the voltage corresponding to 0 dBm is different.
04.6Worked load examples
Let Vth=2 Vpp and Rs=50 Ω.
A high-impedance oscilloscope observing the generator directly therefore sees approximately the open-circuit voltage, not the matched-load value, unless a 50 Ω termination is intentionally present.
04.7During a frequency sweep, the DUT can change the applied input amplitude
If ZL depends on frequency, then
Even with a constant generator setting, the DUT input voltage can vary through the sweep. This is one reason transfer measurements should use the measured input and output at each frequency when accuracy matters:
Assuming the generator display equals the DUT input can inject a systematic frequency-dependent error.
04.8At sufficiently high frequency, the cable is not a lumped wire
The Thévenin divider is a low-frequency/lumped model. When cable electrical length becomes significant, characteristic impedance and reflections matter.
For a transmission line with characteristic impedance Z0 terminated by ZL, the load reflection coefficient is
A matched load ZL=Z0 gives Γ=0. This later becomes a central RF/VNA concept. MS-02 only uses it here to mark the boundary of the lumped source model.
04.9Source reference/ground is part of the same connection map
A generator output may have its shield/common tied to chassis/earth, isolated to some rating, or implemented differently. The actual topology must be checked exactly as in chapter 01.
Connecting a generator can therefore introduce an earth path even before the oscilloscope is attached. When both generator and scope are ground referenced, their cable shields may already connect DUT reference nodes through the laboratory earth/chassis network.
The source model must include both impedance and reference topology.
04.10Source checklist & mastery exercises
- Identify the physical output impedance from the generator specification.
- Identify what load the displayed amplitude assumes.
- Choose amplitude unit explicitly: Vpp, Vpk, Vrms, high/low levels or dBm with load.
- Check DC offset and high/low limits.
- Estimate or measure DUT input impedance over frequency.
- Map output common/shield/chassis/earth connections.
- Measure actual Vin at the DUT when transfer accuracy matters.
- Vth=4 Vpp, Rs=50 Ω, RL=50 Ω. Find Vload.
- Repeat for RL=950 Ω.
- A generator displays 1 Vpp “into 50 Ω” but is connected to a very high impedance. What voltage is expected for an ideal 50 Ω source?
- Convert a 2 Vpp sine to Vpk and Vrms.
- What Vpp sine corresponds to 0 dBm into 50 Ω?
- Why can dBm not be converted to voltage without impedance?
- Why can Vin vary in an RLC sweep even if the generator amplitude setting is constant?
- What model replaces the simple divider when cable propagation/reflections are important?
Solutions
1. 2 Vpp.
2. 4×950/(950+50)=3.8 Vpp.
3. Approximately 2 Vpp open-circuit/high-Z.
4. Vpk=1 V and Vrms=1/√2≈0.7071 V.
5. 0.6325 Vpp.
6. dBm specifies power; voltage depends on the resistance through Vrms=√(PR).
7. The DUT impedance is frequency dependent, so the source/DUT voltage divider changes with frequency.
8. A transmission-line model using characteristic impedance and reflection coefficients.
Chapter 05 will close MS-02 by combining probe response, scope bandwidth, sample rate and waveform rise time into one reproducible measurement-confidence workflow.