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Common causes and remedies for oscillations when designing amplifiers
Date:May 2, 2025    Views:73

   Analog circuit designers take great pains to make amplifiers stable when designing them. However, in the real world, there are always many situations that cause amplifiers to oscillate
    Different types of loads may cause the amplifier to sing;
    Poorly designed feedback networks can cause instability
    Inadequate power bypasses can also cause problems
    The input and output as a single-port system may also self-oscillate;
    ……
    In order to solve these problems, today we will discuss with you the common causes of oscillation and remedies.


Basic knowledge
    Figure 1a shows a block diagram of an off-rail to rail amplifier. The input controls the gm box, which drives the gain node and is buffered at the output. Compensation capacitor Cc is the main frequency response component. The Cc return pin should be grounded, if there is such a pin; But operational amplifiers are traditionally ungrounded, and capacitor current returns to one or both power sources. Figure 1b is a block diagram of the simplest rail-to-rail output amplifier. The output current of the input box gm is sent through a "current coupler", which splits the drive current into two parts and provides it to the output transistor. The frequency response is determined by two Cc/2s, which are actually in parallel.

 Figure 1a: Typical track-to-track operational amplifier topology


Figure 1b: Typical rail-to-rail operational amplifier topology
    These two topologies represent the vast majority of operational amplifiers that use external feedback. Figure 1c shows the frequency response of our ideal amplifier, with the two circuits behaving similarly despite their different electrical principles. The unipolar point compensation formed by gm and Cc provides a unit gain bandwidth product frequency of GBF = gm/(2πCc). The phase lag of these amplifiers decreases from -180 ° to -270 ° near GBF/Avol, where Avol is the amplifier's open-loop DC gain. When the frequency is much higher than this low frequency, the phase stays at -270 °. This is known as "main pole compensation", in which the Cc pole dominates the frequency response, hiding the various frequency limits of the active circuit.



Figure 1c: Idealized op amp frequency response
    Figure 2 shows the open-loop gain and phase response of the LTC6268 amplifier with variation in frequency. The LTC6268 is a small, low-noise 500MHz amplifier with a rail-to-rail output and only 3fA bias current, which serves as a good example of how a real amplifier behaves. The -90 ° phase lag of the main pole compensation starts at about 0.1MHz, reaches -270 ° at about 8MHz, and shifts down to more than -270 ° beyond 30MHz. In fact, in addition to the basic dominant compensation lag due to the extra gain stage and output stage, all amplifiers have high frequency phase lag. Typically, the starting point for additional phase lag is around GBF/10.

Figure 2: The gain and phase of LTC6268 with frequency
    The stability of the feedback is a matter of loop gain and phase, or Avol times the feedback coefficient, in short, loop gain.If we connect the LTC6268 in a unit-gain configuration, the output voltage feeds back 100%. At very low frequencies, the output is negative of the "-" input, or the phase lag is -180 °. Compensation adds another -90° lag through the amplifier, introducing a -270 ° lag from the "-" input to the output. The oscillation occurs when the loop phase lag increases to ±360° or its multiple, and the loop gain is at least 1V/V or 0dB. The phase margin is a measure of how much the phase lag differs from 360° when the gain is 1V/V or 0dB. Figure 2 shows that the phase margin is about 70° at 130MHz (10pF red curve). This is a very healthy number, and phase margins as low as about 35° are feasible.

    A less frequently discussed topic is gain margin, although this is an equally important parameter. When the phase margin is reduced to zero at some higher frequency, the amplifier will oscillate if the gain is at least 1V/V or 0dB. As shown in Figure 2, when the phase is reduced to 0° (or a multiple of 360°, or -180 ° as shown in the figure), the gain is about -24dB at around 1GHz. This is a very low gain, and no oscillation occurs at this frequency. In practice, one wants a gain margin of at least 4dB.


De-compensated amplifier
    Although the LTC6268 is fairly stable under unity-gain conditions, there are a small number of deliberately unstable op amPs. By designing the amplifier compensation to be stable only at higher closed-loop gain, the design tradeoff provides higher conversion rates, wider GBF, and lower input noise than the unit-gain compensation scheme. Figure 3 shows the open-loop gain and phase of the LTC6230-10. The amplifier is intended for use with a feedback gain of 10 or greater, so the feedback net will attenuate the output by at least a factor of 10. With this feedback network, we can find the frequency at an open-loop gain of 10V/V or 20dB and find a phase margin of 58° at 50MHz (±5V power supply). At unit gain, the phase margin is only about 0° and the amplifier oscillates.



Figure 3: The gain and phase of the LT6230-10 with frequency
    One observation is that all amplifiers are more stable when provided with a closed-loop gain greater than the minimum stable gain. Even a gain of 1.5 will make an amplifier with stable unit gain much more stable.

Feedback network
    Speaking of oscillations, the feedback network itself can also cause oscillations. Note that in Figure 4, we put a parasitic capacitor in parallel with the feedback divider. This is inevitable, each terminal of each component on the board has about 0.5pF parasitic capacitance to the ground, and there is a parasitic capacitance of the line.
Figure 4: Parasitic capacitors are loaded onto the feedback network
    In fact, the minimum capacitance of the node is 2pF, and there are about 2pF capacitance per inch of the line. The cumulative parasitic capacitance can easily reach 5pF. Consider the LTC6268 that offers +2 gain. To reduce the power, we set the Rf and Rg values to a fairly high 10kΩ. For Cpar = 4pF, the feedback network has a pole at 1/(2π*Rf||Rg*Cpar) or 8MHz. Using the fact that the feedback network has a phase lag of -ATAN (f/8MHz), we can estimate that at around 35MHz, the loop will have a phase lag of 360°, then the amplifier will have a phase lag of -261 ° and the feedback network will have a phase lag of -79 °. At this phase and frequency, the amplifier still has a gain of 22dB, while the divider gain is

    At 0° phase, 22dB of the amplifier is multiplied by -19dB of the feedback divider to produce a +3dB loop gain, and the circuit oscillates. In order to function properly in the presence of parasitic capacitance, we must reduce the value of the feedback resistor so that the feedback pole far exceeds the unit-gain frequency of the loop. The ratio of poles to GBF must be at least 6 times.
    The op amp input itself may also have a considerable capacitance, as does the Cpar. In particular, low-noise and low-VOS amplifiers have large input transistors and may have larger input capacitors than other types of amplifiers, which are loaded onto the amplifier feedback network. We need to consult the data table to understand how much capacitor will be in parallel with the Cpar. Fortunately, the LT6268 has only a 0.45pF capacitance, which is very low for such a low noise amplifier. A circuit with parasitic capacitors can be simulated using ADI's free macro model running on LTspice®.

图 5 显示了提高分压器电容容限的方法。


Figure 5: Ways to reduce the impact of Cpar
    ● Figure 5a shows a non-negative output amplifier configuration with added Rin. The Vin is assumed to be a low impedance source (<
    ● Figure 5b shows a negative output configuration. Rg still performs loop attenuation without changing the closed-loop gain. In this case, the input impedance is free from "Rg" interference, but noise, offset, and bandwidth parameters deteriorate.
    ● Figure 5c shows the optimal method for compensating Cpar in the in-phase amplifier. If we set Cf* Rf = Cpar * Rg, we have a "compensated attenuator" so that the feedback divider now has the same attenuation at all frequencies and solves the Cpar problem. Mismatches in the product will cause "bumps" in the amplifier's passband and "shelf" in the response curve (where the low-frequency response is flat but changes to another flat line segment near f = 1/2 * Cpar * Rg). Figure 5d shows the equivalent Cpar compensation for a negative output amplifier.         The frequency response must be analyzed to find a correct Cf, and the bandwidth of the amplifier is part of that analysis.
     Here are some reviews of current feedback amplifiers (CFA) in turn. If the amplifier in Figure 5a is a CFA, then "Rin" does little to change the frequency response because the negative input is a very low impedance and actively copies the positive input. The noise indicator will be slightly degraded, and the additional negative input bias current will actually be in the form of Vos/Rin. Again, the circuit in Figure 5b is not altered by "Rg" in terms of frequency response. The inverting input is not just a virtual ground, it is a real ground low impedance and has allowed Cpar (negative output mode only!). . The DC error is similar to the situation shown in Figure 5a. Figure 5c and 5d May be the preferred solution for voltage input opamps, but CFA does not allow a direct feedback capacitor without oscillation at all.

Load problem
    Just as feedback capacitors can harm the phase margin, so can load capacitors. Figure 6 shows how the LTC6268 output impedance varies with frequency at several gain setpoints. Note that the unit-gain output impedance is lower than the output impedance at higher gain. Full feedback enables the open-loop gain to reduce the inherent output impedance of the amplifier. Therefore, in Figure 6, the output impedance at a gain of 10 is generally 10 times that of the output impedance at unit gain. Since the feedback attenuator reduces the loop gain, the loop gain is 1/10, otherwise it would reduce the closed-loop output impedance. The open-loop output impedance is about 30, which is evident in the high frequency flat region of the curve with a gain of 100. In this region, from the gain bandwidth frequency /100 or so to the gain bandwidth frequency, there is not enough loop gain to reduce the open-loop output impedance.


Figure 6: The output impedance of the LTC6268 varies with frequency for three gain scenarios
    Capacitor load will cause phase lag and amplitude attenuation of open-loop output impedance. For example, a 50pF load and our LTC6268 30 output impedance form another pole at 106MHz, where the output has a -45 ° phase lag and -3dB attenuation. At this frequency, the amplifier has a -295 ° phase and a 10dB gain. Assuming the unity-gain feedback is used, we do not fully achieve oscillation because the phase does not reach ±360° (at 106MHz). However, at 150MHz, the amplifier has a 305° phase lag and a 5dB gain. The output pole has a phase
    –atan(150MHz/106MHz) = –55°
    And a gain

    Multiplying the gain cyclically, we get 360° phase and +0.2dB gain, again an oscillator. 50pF appears to be the minimum load capacitance that will force the LTC6268 to oscillate.
    The most common way to prevent the load capacitor from causing oscillations is to simply give the capacitor a small resistance value in series after the feedback connection. Resistance values of 10Ω to 50Ω will limit the phase lag that can be caused by capacitive loads and isolate the amplifier from low capacitive impedances at very high speeds. Disadvantages include DC and low-frequency errors that vary with the load resistance characteristics, limits on the capacitive load frequency response, and signal distortion if the load capacitance is not constant as the voltage changes.
    Increasing the closed-loop gain of the amplifier often prevents oscillations caused by the load capacitance. Running the amplifier at a higher closed-loop gain means that at frequencies where the loop phase is ±360°, the feedback attenuator also attenuates the loop gain. For example, if we use the LTC6268 with a closed-loop gain of +10, then we see that the amplifier has a gain of 10V/V or 20dB at 40MHz with a phase lag of 285°. To excite the oscillation, an output pole is required, resulting in an additional 75° lag. By -75 ° = -ATAN (40MHz/Fpole) → Fpole = 10.6MHz, we can find the output pole. This pole frequency is derived from a 500pF load capacitor and an output impedance of size 30. The output pole gain is

    Since the unloaded open-loop gain is 10, we get that the loop-wound gain at the oscillation frequency is 0.26, so this time we do not produce an oscillation, at least not one caused by a simple output pole. Thus, by increasing the closed-loop gain, we increase the load capacitance tolerance from 50pF to 500pF.
    In addition, unterminated transmission lines are also very bad loads because they introduce "runaway" impedance and phase changes that repeat with frequency (see the impedance of an unterminated 9-foot cable in Figure 7).


Figure 7: Impedance and phase of unterminated coaxial cable
    If your amplifier can safely drive the cable under some low-frequency resonant condition, it is likely to oscillate at some higher frequency because its own phase margin is reduced. If the cable must be unterminated, a "back-match" resistor in series with the output terminal can isolate the extreme impedance changes of the cable. In addition, even if the transient reflection from the unterminated end of the cable is exactly recoiled back into the amplifier, if the resistance value of the backward matching resistor matches the characteristic impedance of the cable, then the resistor can properly absorb this energy. If the backward matching resistor does not match the cable impedance, then some energy is reflected from the amplifier and the terminals, all the way back to the unterminated end. When the energy reaches that end, it is again quickly reflected back to the amplifier, and as a result, there is a series of pulses that bounce back and forth, but each time there is a attenuation.
    Figure 8 shows a more complete output impedance model. The ROUT term is the same as we discussed in LTC6268, which is also 30Ω, and here we add another Lout term. This is a combination of physical inductance and electronic equivalent inductance. The physical package, bonding wire, and external inductance add up to 5nH to 15nH, and the smaller the package, the smaller the number.




Figure 8: Inductive components of the amplifier output impedance
    Any amplifier has a 20nH to 70nH electrical inductance, especially bipolar devices. The finite Ft of the device turns the parasitic base resistance of the output transistor into an inductor. The danger is that Lout and CL may interact to form a series resonant circuit, then the same problem comes again, if there is no greater phase lag in the loop, the impedance of the series resonant circuit may drop to a level that Rout cannot drive, which may produce oscillations. For example, set Lout = 60nH and CL = 50pF. Resonant frequency



    Located just inside the LTC6268 passband. In fact, this series resonant circuit is loaded onto the output during resonance, seriously altering the phase of the loop near the resonant frequency. Unfortunately, Lout is not mentioned in the amplifier's data sheet, but its effect can sometimes be seen on the open-loop output impedance diagram. In short, this effect is not important for amplifiers with bandwidths less than 50MHz or so.
    One solution is shown in Figure 9. Rsnub and Csnub form what is called a "shock absorber", whose purpose is to reduce the Q value of the resonant circuit so that the resonant circuit does not add a very low resonant impedance to the amplifier output. The value of Rsnub is usually estimated as the reactance of CL at resonance (in this case -j35Ω) to reduce the Q value of the output resonant circuit to about 1. Resize Csnub so that Rsnub is fully inserted at the output resonant frequency, i.e., Csnub's reactance <.


Figure 9: Using an output shock absorber
    The negative input of the current feedback amplifier is actually a buffer output that will also exhibit a series of features as shown in Figure 8. Thus, the input, like an output, may be self-oscillating with Cpar. Cpar and any associated inductance must be minimized. Unfortunately, shock absorbers at the negative input will change the closed-loop gain with frequency changes, so they are not practical.

Strange impedance
    Many amplifiers have a slightly abnormal input impedance at high frequencies. This is most true of amplifiers with two input transistors in series, such as the Darlington configuration. Many amplifiers have npn/pnp transistor pairs at the input, which behave with frequency similar to the Darlington configuration. The real part of the input impedance becomes negative at some frequencies (generally much higher than GBF). The inductive source impedance will resonate with the input and board capacitors, and a negative real component may cause oscillations. When driven with an unterminated cable, this can also cause oscillations at many repeat frequencies. If the input inevitably uses a long inductive wire, then several resistors in series that can absorb energy can be used to disconnect the wire, or a medium impedance shock absorber (about 300Ω) can be installed on the amplifier input lead.

Power source

    The final source of oscillation to consider is the power bypass. Figure 10 shows a portion of the output circuit. LVS+ and LVS - are unavoidable series inductors for packaging, IC bonding wires, the physical length of the bypass capacitor (which is inductive like any conductor), and circuit board wiring. Also included are external inductors that connect the local bypass component to the rest of the power bus (if not the power plane). Although 3nH to 10nH May not seem like much, at 200MHz, it is 3.8 to j12Ω. If the output transistor conducts a large high-frequency output current, there will be a voltage drop at both ends of the supply inductor.

Figure 10: Power bypass details
    The rest of the amplifier requires a noise-free power supply because these parts cannot suppress the power supply noise as the frequency changes. In Figure 11 we can see the frequency dependent power supply rejection ratio (PSRR) of the LTC6268. In all op-amps, because there is no ground pin, the compensation capacitors are connected to the power supply, which will couple the power supply noise into the amplifier, and the gm must counteract this noise. Due to compensation, PSRR decreases with 1/f, and power suppression actually increases after 130 MHZ. At 200MHz, due to the increase of PSRR, the output current may interfere with the supply voltage inside the LVs inductor, and through the amplification of PSRR, the interference becomes a strong amplifier signal, driving the output current, generating an internal power signal, etc., resulting in amplifier oscillation. This is why the power supply for all amplifiers must be carefully bypassed with very small inductance lines and components. In addition, the power bypass capacitor must be much larger than any load capacitor.

Figure 11: Power suppression with frequency for LTC6268
    If we consider frequencies around 500MHz, then 3nH to 10nH becomes j9.4Ω to j31.4Ω. This is sufficient for the output transistor to generate self-oscillation by its inductance and IC component capacitance, especially at large output currents (transistor gm and bandwidth increase). Because transistors produced with today's semiconductor manufacturing processes have a large bandwidth, special attention needs to be paid, at least at large output currents.

Conclusion
    In summary, designers need to consider the parasitic capacitance and inductance associated with each op amp terminal, as well as the nature of the load. Amplifiers are designed to be stable in nominal environments, but each application requires its own analysis.





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