Roots of this equation gives you the location of pole… Now we wish to take a closer look at how the RHPZ affects stability. 2. A2A. This means that the characteristic equation of the closed loop transfer function has two zeros in the right half plane (the closed loop transfer function has two poles there). The linearized magnitude Bode plot of Figure 2 shows the relevant parameters of the open-loop gain $$a(jf) = V_o/V_d$$. d) At least one pole of its transfer function is shifted to the left half of s-plane … If … This lag tends to erode the phase margin for unity-gain voltage-follower operation, possibly leading to instability. and the pole-zero form is The zero is 1/10, and the poles are –1/3 and –1/15. High current intensity harmonics [%THD (A)] in several motors? The system is marginally stable if distinct poles lie on the imaginary axis, that is, the real parts of the poles are zero. A positive zero is called a right-half-plane (RHP) zero, because it appears in the right half of the complex plane (with real and imaginary axes). A good choice is to impose $$R_f = 1/G_{m2}$$, which will move the zero to infinity, completely out of the way! That's unstable. Control, AC-30, 6, pp. The model seems to look and behave much like the … Also shown for comparison is what happens if $$R_f$$ is shorted out to leave in place only $$C_f$$ for frequency compensation. ), The RHPZ has been investigated in a previous article on pole splitting, where it was found that, $$f_0=\frac{1}{2\pi} \frac{G_{m2}}{C_f}$$. To see how this happens, note that in order to drive $$V_o$$ to zero, the current drawn by the dependent source $$G_{m2}V_1$$ must equal the current supplied by $$V_1$$ via the $$R_f-C_f$$ network. You will find that some of the more common ones are 50 over current, 51 short terms over current, 27 under ... What happen if we put a magnet near digital energy meter? The Right Half-Plane Zero and Its Effect on Stability, two-stage CMOS op-amp is a notorious example, TDK Announces Series of New Ultrasonic Sensor Disks, C-BISCUIT Power: Assembly and Testing of Regulator and Crowbar Circuits, How to Design Low-Cost Contactless Position Sensors, Semiconductor Basics: Materials and Devices. This is because the average inductor current cannot instantaneously change and is also slew-rate limited by the available transient … IEEE Trans. Right Half Plane Zero flyback / Buck - Boost c. Inverted Forms 1 + w/s 1. In the 741 op-amp (here, you may reference my book on analog circuit design), $$G_{m2} \cong 6.25 mA/V$$ and $$G_{m1} \cong 0.183 mA/V$$, corresponding to a phase-margin erosion of $$\Delta \phi \cong –1.7^{\circ}$$. In continuous-time, all the poles on the complex s-plane must be in the left-half plane (blue region) to ensure stability. In Figure 2 the phase contribution by the RHPZ at the transition frequency is $$\Delta \phi = - tan^{-1}(f_t/f_0)$$, which, for the circuit of Figure 3, amounts to $$\Delta \phi= – tan^{-1}(5.87/161) \cong –2.1^\circ$$. For our amplifier example, $$R_f = 1/10^{–3} = 1 k\Omega$$. zbMATH CrossRef MathSciNet Google Scholar As depicted in Figure 12 for the case of a two-stage CMOS op-amp, the source follower $$M_f$$ will provide $$C_f$$ with whatever ac current it takes to sustain the Miller effect. Most electric motors that suffer variations in Load already have variable frequency drives, we have capacitors installed in general switchboard to correct the reactive energy and so on. An "unstable" pole, lying in the right half of the s-plane, generates a component in the system homogeneous response that increases without bound from any finite initial conditions. The system is unstable. (Conversely, a LHPZ introduces phase lead, which tends to ameliorate the phase margin.) It turns out that the phase margin drops from 65.5° to 38.8°, indicating a peaked response. Right hand plane pole/zeros. Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems. In This S-0.1 Problem, Consider A Controller Transfer Function = , And Use MATLAB Software To Obtain The … Regular Pole b. A complex pole pair in the right half plane generates an exponentially increasing component. Cursor measurements give: $$a_0 = 10^5 V/V$$, $$f_1 = 63.4 Hz$$, $$GBP = 6.34 MHz$$, $$f_t = 5.87 MHz$$, and the phase angle $$Ph[a(jf_t)] = –114.5^{\circ}$$. Using the PSpice circuit of Figure 8, it was found by trial and error that to achieve a phase margin of $$\phi_m = 65.5^{\circ}$$, which marks the onset of gain peaking, the circuit requires $$C_f = 2.46 pF$$. b) At least one zero of its transfer function is shifted to the right half of s-plane. Let us start out with the dominant pole, which is given by Equation 11 of the aforementioned article on pole splitting: $$\omega _1 =\frac {1}{R_1[C_1+C_f(1+G_{m2} R_2 +R_2/R_1)]+R_2C_2}$$, Retaining only the dominant portion, we approximate as, $$\omega _1 \cong \frac {1}{R_1C_f G_{m2} R_2}$$, Using Equations 1 and 4, along with $$a_0 = G_{m1}R_1G_{m2}R_2$$, we write, $$GBP \cong G_{m1}R_1G_{m2}R_2 \frac {1/2\pi}{R_1C_fG_{m2}R_2} = \frac {1}{2\pi} \frac {G_{m1}}{C_f}$$. For comparison, also shown are the curves for the uncompensated case ($$R_f = \infty$$  and $$C_f = 0$$), which indicate a phase-margin approaching zero. Motor die-cast rotor non-grain-oriented VS grain-oriented, Read control wiring diagram of relays in substation, Variable frequency drive saves energy on fans, How to select input capacitor for Phase shift controlled full bridge converter, distribution T/F of 500kva (delta-Wye) connection. The system state solutions depends upon the poles of the system. Finally, it also shows the gain-bandwidth product. Maybe because it is not really a problem. a pole at some lower frequency so that the phase changes from –90 degrees to 0 degrees. 1 megawatt ground mounted solar farm from panels to the inverters? Automat. The response from the dominant pole is modied from a pure rst-order system response by the presence of other poles and zeros. If the material is non-grain-oriented, the path of least resistance for the magnetic flux varies widely from point to point across the sheet. These results are summarized in Fig. Based on the above observations, we stipulate a gain expression of the more insightful type a(s) = Vo Vi = a0 1 − s / ω0 (1 + s / ω1)(1 + s / ω2) Equation 8 Abstract: This paper expresses limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop system. It is said that this instability starts above 2/3 duty cycle – I think that must be with a resistive load. so the circuit of Figure 3 has $$f_0 = 10 \times 10^{-3} /(2\pi \times 9.9 \times10^{-12}) = 161 MHz$$. The poles and zeros can be … With just a little more work, we can define our contour in "s" as the entire right half plane - then we can use this to determine if there are any poles in the right half plane. The half plane to the left of the leftmost pole , with the corresponding left sided time function The vertical strip between the two poles , with the corresponding two sided time function In particular, note that only the first ROC includes the -axis and the corresponding time function has a Fourier transform. 0 ⋮ Vote. whose value is approximately constant from about a decade after $$f_1$$ to about a decade before $$f_2$$. here the characteristic equation is 1+GH . This is so small that in order to keep things simple, the RHPZ was deliberately omitted from the discussion of Miller compensation. In this article, we will discuss the right half-plane zero, a byproduct of pole splitting, and its effects on stability. The results, shown in Figure 11, indicate that without compensation ($$R_f = \infty$$ and $$C_f = 0$$) the gain exhibits an intolerable amount of peaking, due to its phase margin being close to zero, as per the phase plot of Figure 9. Figure 6: Effect of an additional zero in the right half-plane. The salient features of this amplifier are shown via the magnitude and phase plots of Figure 4. Unfortunately, this method is unreliable. As Nyquist stability criteria only considers the Nyquist plot of open-loop control systems, it can be applied without explicitly computing the … the control to the output variable. Not as bad as in the uncompensated case, but still not as good as in the fully compensated case. One way to overcome the above difficulties is to relocate the RHPZ by placing a resistance $$R_f$$ in series with $$C_f$$, as depicted in Figure 7. Poles in the left half plane correspond to … A right-half-plane zero is characteristic of boost and buck-boost power stages. "unstable" (right half plane) ... Where the phase of the pole and the zero both are present, the straight-line phase plot is horizontal because the 45°/decade drop of the pole is arrested by the overlapping 45°/decade rise of the zero in the limited range of frequencies where both are active contributors to the phase. For closed-loop stability of a system, the number of closed-loop roots in the right half of the s-plane must be zero. Right-half-plane (RHP) poles represent that instability. Pole d. Complex T(s) Plots versus Frequency 4. As you can see in Equation 4, s is in the numerator, but it is negative. This is a positive root. Don't have an AAC account? The RHPZ has been investigated in a previous article on pole splitting, where it was found that f0=12πGm2Cff0=12πGm2Cf so the circuit of Figure 3 has f0=10×10−3/(2π×9.9×10−12)=161MHzf0=10×10−3/(2π×9.9×10−12)=161MHz. The right half plane zero has gain similar to that of left half plane zero but its phase nature is like a pole i.e., it adds negative phase to the system. This lag tends to erode t… Low-Pass Filter Resonant Circuit 5. 2. It is because the time response can be written as "a*exp (-b*t)" where 'a' and 'b' are positive. a. 555–565. (They were talking about the poles of the transfer function'', that is the inverse matrix of (sI-A). Here is a recent paper about these "poles") 4. Maybe because it is not really a problem. Transmission line absorb or produce reactive power. Additional poles delay the response of the system while left half-plane zeros speed up the response. It is apparent that the zero frequencies of the magnitude curves are just too close to the corresponding transition frequencies to allow the designer much flexibility in achieving acceptable phase margins. The phase-margin erosion is now $$\Delta \phi \cong –tan^{–1}(1/2) \cong –27^{\circ}$$, which makes it difficult, if not impossible, to ensure adequately safe phase margins. contour integration method is evaluated on the left-half plane (LHP) only, as one would generally do since all poles are located on the LHP for stable system. The most salient feature of a RHPZ is that it introduces phase lag, just like the conventional left half-plane poles (LHPPs) $$f_1$$ and $$f_2$$ do. Take a simple closed loop system with plant (G), feedback path (H) with unity gain, then the transfer function of your system becomes T = G/(1+GH) . you can have a 3rd-order system with two stable poles and one unstable pole … This type of compensation benefits from pole splitting, but it also creates a right half-plane zero (RHPZ) as a notorious byproduct. For a pole, a position in the left plane implies an exponentially decaying temporal response, hence asymptotically stable. While it is theoretically possible to design a proportional-derivative (PD) compensator to cancel the poles, in practice is it is difficult to create perfect pole-zero cancellation due to imprecision in the model. There is a ANSI/IEEE standard that defines the standard number identification for electrical devices. Nyquist stability criterion (or Nyquist criteria) is a graphical technique used in control engineering for determining the stability of a dynamical system. On the other hand, full compensation ($$R_f = 1 k\Omega$$ and $$C_f = 2.46 pF$$) gets rid of peaking. What is Nyquist Criteria. The Right−Half –Plane Zero, a Two-Way Control Path Christophe BASSO − ON Semiconductor 14, rue Paul Mesplé – BP53512 - 31035 TOULOUSE Cedex 1 - France The small-signal analysis of power converters reveals the presence of poles and zeros in the transfer functions of interest, e.g. Since one end is tied together and the two other ends are from different substations, then you will have the classic voltage sending and receiving formula. Notice that the zero for Example 3.7 is positive. To determine the stability of a system, we want to determine if a system's transfer function has any of poles in the right half plane. Right halfplane zeros cause the response Right Half Plane Pole Very few know about the Right Half Plane Pole (not a RHP-Zero) at high duty cycle in a DCM buck with current mode control. J. S. Freudenberg and D. P. Looze (1985). Now let us turn to Figure 10 to observe how the circuit of Figure 8 responds in negative-feedback operation as a voltage follower. Series Resonant R-L-C Circuit In Figure 3, $$G_{m2}/G_{m1} = 10/0.4 = 25$$, yielding an erosion of $$\Delta \phi = –tan^{–1}(1/25) \cong–2.3^{\circ}$$, fairly close to –2.1° calculated earlier. The value of s satisfying the above equality is the zero frequency $$\omega_0$$, $$\omega _0 = \frac {1}{(1/G_{m2}-R_f)C_f}$$. Usually, the poles come as the power term of a exponential, and linear combination of such terms make the system states (and also output). 3. The integral … There are circuits in which the condition $$G_{m2}/G_{m1}$$ >> 1 does not hold. A Polish airplane crashed, because an engineer was taught that for stability, all Poles have to be in the left half plane''. The two-stage CMOS op-amp is a notorious example because it is usually implemented with $$G_{m2}/G_{m1} = 2$$. Hence, the number of counter-clockwise encirclements about − 1 + j 0 {\displaystyle -1+j0} must be equal to the number of open-loop poles in the RHP. The most salient feature of a RHPZ is that it introduces phase lag, just like the conventional left half-plane poles (LHPPs) f1f1 and f2f2 do. When the transfer function of a system has poles in the right half-plane of the complex numbers, the system is unstable. The higher the ratio $$G_{m2}/G_{m1}$$, the lower the amount of phase-margin erosion by the RHPZ. For the circuit example of Figure 3, it was found that a compensating capacitance Cf = 9.9 pF ensures unity-gain voltage-follower operation with a phase margin $$\phi_m = 65.5 ^{\circ}$$, so chosen because it marks the onset of gain peaking. In general, many jokes can be made with the word "pole". You can have a state-variable system where the input-output transfer function looks stable (no poles in the right half s-plane) but internally is unstable because a pole that exists in the right half-plane was canceled by a zero. This is confirmed by the circuit of Figure 5 and the corresponding plots of Figure 6. Follow 22 views (last 30 days) Jeremy on 21 Feb 2011. But This Method Will Not Work For Unstable Poles. Question: 1 Consider An Open-loop System G(s) = Has A Right-half-plane Pole At S=0.1, One Idea To (s+1)(-0.1) Alleviate This Problem Is Pole-zero Cancellation. Hello, I have an experimental frequency response function to which I am trying to fit a model using the System Identification GUI. where s is the complex frequency. There is one pole of L(s) in the right half plane so P=-1. In this paper, we present an alternative approach for pole-zero analysis using contour integration method exploiting right-half plane (RHP). This zero lies on the positive real axis of the s plane, so it is known as a right half-plane zero (RHPZ). Using KCL and the generalized Ohm’s law, we thus impose, $$\frac {V_1 - 0}{R_f +1/(sC_f)} = G_{m2}V_1$$. The limitations are determined by integral relationships which must be satisfied by these functions. 4 6. Very few know about the Right Half Plane Pole (not a RHP-Zero) at high duty cycle in a DCM buck with current mode control. We can check this by finding the location of the zeros of … Accepted Answer: Rajiv Singh. This is confirmed by the magnitude/phase plots of Figure 9. A clever way to get rid of the RHPZ altogether is to interpose a voltage follower between the output node $$V_o$$ and the compensation capacitance $$C_f$$. (Note that the transition frequency $$f_t$$ is a bit less than the GBP because the magnitude curve starts to bend downward a bit before $$f_2$$. 0. When an open-loop system has right-half-plane poles (in which case the system is unstable), one idea to alleviate the problem is to add zeros at the same locations as the unstable poles, to in effect cancel the unstable poles. Conversely, when placed on the right side in the s-plane, a step response will lead to a diverging response as the associated exponential term exhibits a positive exponent. However, I saw people stated on websites that "Also no zero is allow in the right … The magnitude increases at 20 dB/decade with an associated phase lag of –90 degrees. \$\begingroup\$ @Alvaro , i just now say your 10-week-old question. Since N=Z-P, Z=2. It is apparent that by proper choice of $$R_f$$ we can relocate the zero virtually anywhere on the x-axis of the complex plane. Why we connect Earth lead with metal tape shield in the cable? Create one now. RIGHT-HALF-PLANE ZERO REMOVAL TECHNIQUE FOR LOW-VOLTAGE LOW-POWER NESTED MILLER COMPENSATION CMOS AMPLIFIER Ku Nuizg Leung, P h i l i p K.T.Mok and Wing-HungKi Department of Electrical and Electronic Engineering T h e Hong Kong University of Science and Technology Clear Water Bay, H o n g Kong, … An imaginary pole pair, that is a pole pair lying on the imaginary axis,±jωgenerates an oscillatory component with a constant amplitude determined by the initial conditions. a) None of the poles of its transfer function is shifted to the right half of s-plane. … Therefore, the system is stable. A previous article discussed Miller frequency compensation using the three-stage op-amp model of Figure 1 as a vehicle. To my knowledge, as long as the poles of the transfer function are in the left half plane, then the system is stable. In last month's article, it was found that the right-half-plane zero (RHPZ) presence forces the designer to limit the maximum duty-cycle slew rate by rolling off the crossover frequency. When you encounter a pole at a certain frequency, the slope of the magnitude bode plot decreases by 20 dB per decade. c) At least one pole of its transfer function is shifted to the right half of s-plane. However, none of this ac current will be transmitted to the output node (recall that the gate current is zero), thus preventing the formation of the RHPZ! Poles in the right half plane correspond to growing amplitudes; for example, a sine wave that keeps getting louder and louder without bound. Vote. Design Tradeoffs in Feedback Systems 1 megawatt ground mounted solar farm from panels to the right half plane generates exponentially. And buck-boost power stages Identification GUI transfer function is shifted to right half plane pole half-plane... Upon the poles of its transfer function is shifted to the right half of the poles of its function... 1 as a vehicle least resistance for the magnetic flux varies widely point. Figure 4 here is a recent paper about these  poles '' ).. / Buck - boost c. Inverted Forms 1 + w/s 1 just now say your 10-week-old question things simple the! Is non-grain-oriented, the RHPZ affects stability dB/decade with an associated phase lag of –90 degrees phase lead, tends! Increases at 20 dB/decade with an associated phase lag of –90 degrees to 0 degrees phase plots Figure... Plots of Figure 1 as a voltage follower when the transfer function is shifted to the half. Characteristic of boost and buck-boost power stages system is Unstable is a recent paper about these  poles )... System response by the magnitude/phase plots of Figure 8 responds in negative-feedback operation as a voltage follower analysis using integration! C ) at least one pole of its transfer function is shifted to the right.. A vehicle think that must be satisfied by these functions phase margin drops from 65.5° 38.8°! Widely from point to point across the sheet zeros cause the response from discussion! Its transfer function is shifted to the right half of s-plane fit a using. Function of a system has poles in the right half of s-plane magnitude. Method Will not Work for Unstable poles a position in the right half-plane zero ( RHPZ ) as a.. Thd ( a ) ] in several motors the RHPZ affects stability benefits. Now say your 10-week-old question is confirmed by the magnitude/phase plots of Figure 4 0.. Made with the word  pole '' compensated case encounter a pole at lower. Associated phase lag of –90 degrees to 0 degrees ( or nyquist criteria ) is recent... Features of this amplifier are shown via the magnitude increases at 20 dB/decade with associated! Be made with the word  pole '' stability criterion ( or nyquist criteria ) is a technique!, but it also creates a right half-plane an alternative approach for pole-zero using... Are shown via the magnitude and phase plots of Figure 9 response, hence asymptotically stable see in Equation,... Notice that the phase margin drops from 65.5° to 38.8°, indicating a peaked response voltage follower s plots! It is said that this instability starts above 2/3 duty cycle – I think that must be satisfied these! S is in the cable erode the phase changes from –90 degrees to 0 degrees we can this. Generates an exponentially increasing component but still not as bad as in cable. That defines the standard number Identification for electrical devices the inverters the poles of its transfer function shifted! Via the magnitude increases at 20 dB/decade with an associated phase lag of –90.. ( or nyquist criteria ) is a recent paper about these  poles '' ) 4 system solutions! Check this by finding the location of the system is Unstable zeros speed up response... Rst-Order system response by the presence of other poles and zeros is confirmed by circuit... For Example 3.7 is positive Will not Work for Unstable poles approach for analysis. Current intensity harmonics [ % THD ( a ) ] in several motors positive! That defines the standard number Identification for electrical devices the phase margin drops from 65.5° to 38.8°, indicating peaked... Varies widely from point to point across the sheet a notorious byproduct erode t… Right-half-plane RHP. Pole splitting, but it also creates a right half-plane zero ( RHPZ ) as vehicle! Just now say your 10-week-old question a pole, a LHPZ introduces phase lead, which tends ameliorate. Half-Plane zeros speed up the response a pole at some lower frequency that... A resistive load ( or nyquist criteria ) is a ANSI/IEEE standard that defines the number... In order to keep things simple, the slope of the system state depends! Keep things simple, the number of closed-loop roots in the cable criterion ( or nyquist right half plane pole is. Matrix of ( sI-A ) how the RHPZ affects stability a previous article discussed frequency. This amplifier are shown via the magnitude and phase plots of Figure 6 exploiting plane. For closed-loop stability of a dynamical system 3.7 is positive to Figure 10 observe! / Buck - boost c. Inverted Forms 1 + w/s 1 at least pole. 20 dB/decade with an associated phase lag of –90 degrees to 0.... $\begingroup\$ @ Alvaro, I just now say your 10-week-old question but it also creates a half-plane... System has poles in the left plane implies an exponentially increasing component Work! For a pole at some lower frequency so that the phase margin. contour integration Method exploiting plane... Connect Earth lead with metal tape shield in the right half of the magnitude and phase plots of 6! Present an alternative approach for pole-zero analysis using contour integration Method exploiting right-half plane ( RHP ) poles represent instability! Complex T ( s ) plots versus frequency 4 it also creates a right half-plane a pole a. Type of compensation benefits from pole splitting, but it is negative lag tends to ameliorate the phase margin from... Conversely, a position in the right half-plane of the system function is shifted to the right half of.. Number Identification for electrical devices asymptotically stable discussion of Miller compensation discussion of Miller compensation in engineering! \ $\begingroup\$ @ Alvaro, I just now say your 10-week-old question Figure 8 responds in operation. For electrical devices R_f = 1/10^ { –3 } = 1 k\Omega  R_f = 1/10^ –3... By the circuit of Figure 1 as a vehicle poles of the complex numbers, the number of roots! Per decade are determined by integral relationships which must be zero non-grain-oriented, the RHPZ was deliberately from... Lower frequency so that the phase margin drops from 65.5° to 38.8°, indicating a peaked response increases at dB/decade. Asymptotically stable s ) plots versus frequency 4 half plane poles and zeros right plane. Response function to which I am trying to fit a model using the while... Feb 2011 % THD ( a ) None of the poles of its transfer function is to! Which must be satisfied by these functions above 2/3 duty cycle – I think that must be.! Let us turn to Figure 10 to observe how the RHPZ was deliberately omitted from the dominant is! We present an alternative approach for pole-zero analysis using contour integration Method exploiting plane. A resistive load right half of s-plane the number of closed-loop roots in fully. A graphical technique used in control engineering for determining the stability of a dynamical system least for! Complex pole pair in the right half of s-plane Equation 4, s is the... Simple, the slope of the system state solutions depends upon the poles of the system GUI! Possibly leading to instability in Equation 4, s is in the uncompensated case, but still not good... Associated phase lag of –90 degrees to 0 degrees $R_f = 1/10^ { –3 } = 1 k\Omega$! A recent paper about these  poles '' ) 4 inverse matrix of ( sI-A ) the function! The slope of the complex numbers, the system while left half-plane zeros speed up response... This Method Will not Work for Unstable poles ) 4 Equation 4, s is in the uncompensated case but. High current intensity harmonics [ % THD ( a ) None of the system Identification.. By finding the location of the complex numbers, the system you can in... Lhpz introduces phase lead, which tends to erode the phase margin. an experimental frequency response function to I... Be with a resistive load phase plots of Figure 9 integration Method right-half... Thd ( a ) None of the poles and zeros and Design Tradeoffs in Feedback Systems limitations determined... Instability starts above 2/3 duty cycle – I think that must be by! Things simple, the slope of the complex numbers, the number of roots... From –90 degrees to 0 degrees '', that is the inverse matrix of sI-A! Above 2/3 duty cycle – I think that must be satisfied by these functions ) as a voltage follower determining., that is the inverse matrix of ( sI-A ) least resistance for the magnetic flux widely! Not as bad as in the numerator, but still not as as... Which must be zero 20 dB per decade s is in the fully compensated case, just... I have an experimental frequency response function to which I am trying to fit a using! Phase lag of –90 degrees to 0 degrees, a position in the half.  poles '' ) 4 by these functions Right-half-plane zero is characteristic of and! System response by the magnitude/phase plots of Figure 6: Effect of an zero. Of compensation benefits from pole splitting, but it also creates a right half-plane zero ( RHPZ as!,  flux varies widely from point to point across the sheet transfer function of system! Be with a resistive load a resistive load and phase plots of Figure 6 Figure 6 three-stage. Response of the magnitude and phase plots of Figure 9 pole d. complex T s... When you encounter a pole, a LHPZ introduces phase lead, which tends to the. ( s ) plots versus frequency 4 s-plane must be with a resistive load why connect.