1. PSRR TIPL 1232 TI Precision Labs – Op Amps
Presented by Collin Wells
Prepared by Collin Wells, Art Kay, Ian Williams, and Tim Green
Prerequisites: Input and Output Limitations 1 – 3
(TIPL1130 – TIPL1132)
Hello, and welcome the TI Precision Labs video on power supply rejection. In this video we will discuss how changing the power supply on op amps can introduce a power supply rejection error. We will consider both ac and dc power supply rejection. Finally, we will consider how changing supply voltage can also introduce a common mode error.

2. Referring Error to Input (RTI)
Errors from power supply rejection, common mode rejection, open loop gain, and many other types of errors can be modeled as an input offset voltage connected to the non-inverting input of the op amp. This method of reflecting the error signal to the input simplifies the error analysis as the error sources can be added to find the total error. In practice, the error sources are often added as the square root sum of the squares because the errors are uncorrelated and can be represented as a Gaussian distribution.

3. DC PSRR
The data sheet table provides a typical and maximum dc power supply rejection, abbreviated PSRR. Later we will look at characteristic curves that show ac PSRR. Note that PSRR can be given in V/V, µV/V or in dB. This slide shows a simulation and calculation where the power supply is reduced by 1V. Note that the positive and negative supply are both shifted equally by a 0.5V. In the next slide we will see the implications behind making symmetrical and asymmetrical changes in the power supply.
Power supply rejection in V/V is defined as the change in offset versus the change in supply voltage and is sometimes this is expressed in µV/V. Power supply rejection in decibels is defined as -20 times the log of rejection in V/V. The negative sign makes the decibel version of PSRR a positive number. Looking at this specific example, the simulation shows a 5µV shift in offset for a 1V change in supply voltage. This is exactly what is expected for this example as the specified typical PSRR is 5µV/V for this device.

4. PSRR & CMRR Combined Effects: Supply Symmetry
This slide shows the difference between a symmetric and asymmetric change in the supply voltage. The key thing to understand is that an asymmetric change in the supply voltage translates into a shift in the common mode voltage. A shift in the common mode voltage will introduce a common mode rejection error. To better understand this, first look at the default test condition shown at the far left. This circuit has symmetrical 15V supplies such that the average of the two supplies is 0V. This is the default case and shifts in offset will occur if the power supply or common mode voltage shift from this configuration. In the second case, the supply voltage has been changed symmetrically such that the average voltage is still zero. In both the first and second case, the common mode voltage with respect to ground is zero and the average power supply voltage is zero. If either the common mode voltage with respect to ground or the average supply voltage change, this constitutes a change in the common mode voltage (delta Vcm). So the second circuit does not have a change in common mode voltage because the supply is kept symmetrical, where as the third circuit does have a change in the common mode voltage because the supply change is asymmetrical. In the third case Vee is shifted to 14V but Vcc is maintained at 15V. The average supply voltage is now 0.5V and the common mode voltage with respect to ground is still 0V. This constitutes as change of 0.5V in the common mode voltage which introduces a common mode error as well as a power supply rejection error.

5. Translating µV/V to dB and Vice Versa
This slide summarizes the verious PSRR definitions as well as general mathematical relationships. It is common to see PSRR represented in V/V, µV/V, and in decibels. These equations allow you to make these translations.

6. AC PSRR Simulated Data Sheet
This slide shows the configuration used to simulate ac power supply rejection. Strictly speaking, inverse ac signals should be applied to both supplies so that the instantaneous average supply voltage is zero. This would keep the common mode voltage constant, and no common mode rejection errors would be introduced. In fact, when performing an ac transfer characteristic for this configuration, the common mode errors are ignored by the simulator, where as the common mode errors will be included in transient analysis. From a practical perspective, however, the configuration shown is the most common way that ac PSRR is actually tested. Yes, it is true that this test configuration will include some common mode effects, but often they will be small compared to PSRR. Furthermore, from a practical perspective looking at an ac signal applied to each separate supply is more a more realistic usage case for the device. In this example you can see that the simulated ac PSRR is very close to the characteristic curve from the data sheet.

7. Tina: Use Post Processor
This slide shows how you can use the post processor in Tina Spice to generate the ac PSRR curve. Pressing the button circled in red will initiate the post processor. The post processor allows you to perform mathematics on curves generated by Tina Spice. The PSRR curve is generated by taking one divided by the offset voltage. From a Tina perspective this is effectively the same as taking 20log of the supply voltage change divided by the offset voltage change because the supply voltage is normalized and Tina automatically displays results in decibels.

8. AC PSRR Example
Here we are showing a transient response to an ac power supply voltage. The ac supply voltage is at 1kHz. The ac PSRR curve shows that PSRR is 80dB at 1kHz which translates to 100µV/V. Multiplying the 2Vpp input signal by the 100µV/V yields a 200µVpp input offset voltage. The output can be calculated by multiplying the 200µVpp offset voltage by the gain of 2V/V for an output of 400µVpp. It is important to remember that all bode plots relate to sinusoidal waveforms. Later we will look at applying a non sinusoidal signal to the supply.

9. PSRR Acts Like a High Pass Filter
Vac
PSRR(dB)
PSRR(µV/V)
Vos
Vout
1Vpk, 1kHz 80
100
100µVpk
200µVpk
1Vpk, 10kHz 60
1,000
1mVpk
2mVpk
1Vpk, 100kHz 40
10,000
10mVpk
20mVpk
Lets take a closer look at the ac PSRR curve. The key point here is that the PSRR curve is a rejection not a gain curve. You might look at this graph and think that it is a low pass filter. In fact, if you draw the PSRR curve as a gain in µV/V rather than a rejection in dB you see that it is actually a high pass filter. In other words, the offset error will increase for higher frequencies. The table illustrates this point for a 1Vpk ac power supply signal at three different frequencies. You can see that increasing frequencies the PSRR in decibels decreases where as the PSRR in µV/V increases. Furthermore, the offset error introduced by the power supply signal increases at higher frequencies.

10. AC PSRR – Time Domain
Now lets look at how PSRR works when non-sinusoidal waveforms are applied to an op amps power supply. In practical circuits, a switching power supply ripple can sometimes look like a triangle waveform. So, in the example above a we look at 1Vpk triangle wave is applied to the supply on the OPA132. Surprisingly, the output looks like a 10mVpk square wave. What causes the shape of the waveform to change? Let’s take a closer look.

11. Infinite Series for a Triangle Wave
Before digging into the details, though, let’s review the concept of a Fourier series. Any non-sinusoidal periodic waveform can be created with in infinite series of sinusoidal waveforms of different amplitude and frequency. So, for example, a triangle wave or square wave can be created by adding an infinite series of sinusoidal waveforms together. The example above shows how a triangle waveform can be created by adding five different sinusoidal waveforms. The lowest frequency component is called the “fundamental”. The higher frequency components, called harmonics, are odd multiples of the fundamental frequency and also have smaller amplitude. Notice that although we only have five harmonics, and not a true infinite series, the resultant waveform is clearly a triangle shape. The mathematical fourier series for a triangle waveform is shown here as well as the magnitude of the frequency spectrum. The theory behind a fourier series will be helpful in understanding how the shape on non-sinusoidal waveforms is effected by different types of filters.

12. Input Spectrum vs. Output Spectrum
This slide illustrates how a triangle waveform on an amplifiers power supply can be translated into a square waveform. Remember the PSRR transfer function acts like a high pass filter. Applying the fourier spectrum for a triangle waveform to a high pass filter, the higher frequency components will be boosted. This has the effect of translating the triangle wave spectrum into a square wave spectrum. Another way of thinking of this is that the high pass filter acts like a differentiator. When you differentiate a triangle waveform it changes into a square wave. In this example the triangle wave was translated into a square wave because of the high pass transfer characteristics of the PSRR function. In other cases, the amplifier bandwidth limitations or slew rate limitations may add additional compounding factors that further distort the wave shape. The real point here is not that a triangle wave applied to the supply will translate into a square wave, but rather that the shape of the output waveform may be impacted by the PSRR transfer function as well as other factors.

13. How to Generate the Fourier Spectrum in Tina
The fourier spectrum for any periodic signal can be displayed using the “Fourier Analysis” feature in Tina Spice. This can be useful if you want to see what the harmonic content of you signals is and how it is effected by the device transfer characteristic.

14. Thanks for your time! Please try the quiz.
This video discussed power-supply rejection and how changing the power-supply voltage on op amps introduces a power-supply rejection error. We discussed how to isolate power-supply rejection errors from common-mode errors and the effects of when non-sinusoidal waveforms are applied to an op amps power-supply.
Thank you for time! Please try the quiz to check your understanding of this video’s content.