Calculation of circuits on transimpedance operational amplifiers. Scheme, description

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Calculation of circuits on transimpedance operational amplifiers. Encyclopedia of radio electronics and electrical engineering

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The article presents analytical calculations of circuits with TOC operational amplifiers. In this case, the most modern methods were used using OrCAD and Maple.

Introduction

The main advantage of current feedback amplifiers is their wide operating bandwidth. All other amplifiers use voltage feedback. the gain with feedback for which begins to fall even at very low frequencies (often from 10 Hz) with a decay rate of 20 dB per decade. This behavior leads to large errors at high frequencies. Voltage feedback amplifiers are forced to operate in the frequency domain, where their gain drops off as the gain of the OS with an open loop OS; starts dropping at low frequencies. Current feedback amplifiers do not have this limitation, so they provide the least distortion. The gain decay rate is approximately the same for both types of amplifiers. The model shown in fig. 2 shows the fact that current feedback amplifiers use transimpedance instead of gain. The input current is "mapped" to the output stage and buffered by it. This configuration provides the maximum bandwidth among ICs using the same process technology. Usually amplifiers with OS but current are built on the basis of bipolar transistors, because. their typical scope - high-speed communications, video, etc., as a rule, does not require high input impedances and output voltage range equal to the supply voltage (rail to rail).

Note that the inverting input is coupled to the output stage of the buffer, so it has a very LOW impedance, in order of magnitude equal to that of the emitter follower. The non-inverting input is a buffer input, so it has a high impedance. For a voltage feedback amplifier, the inputs are fed to the base-emitter junctions of a phase inverter (a differential stage powered by a current source). The precise matching of the transistors in the differential stage minimizes input currents and bias voltages, and in this regard, a voltage feedback amplifier has a great advantage. Matching the INPUT and OUTPUT buffer circuits is a daunting task, so current feedback amplifiers are not precise. Their main purpose is high-speed circuits, if for voltage feedback amplifiers the limit is about 400 MHz, then current-coupled amplifiers have an operating bandwidth of up to several gigahertz. A typical operating range for an op amp TOC is from about 25 MHz to several GHz. However, when using such amplifiers, one of their important features should be kept in mind. When designing high-frequency circuits, many designers rely on gain reduction with increasing frequency as a stability factor, rightly believing that a circuit with a gain of less than unity by default is stable. But this is true only for amplifiers with voltage feedback. Current feedback op amps retain their gain as the frequency increases. Therefore, circuits developed on the basis of amplifiers with voltage feedback and working stably with them often become unstable when switching to amplifiers with current feedback. Moreover, the input and feedback resistor of a current-feedback amplifier are susceptible to scratches and capacitance, so pay close attention to board layout.

1. Transimpedance TOS OU

Let's find the transimpedance of the TOS op-amp with open feedback on the inverting input. To do this, we use the measurement scheme (Fig. 1). We will use the simplest single-pole idealized equivalent circuit (Fig. 2) as a model of the OS TOC.
Rice. 1. Scheme for measuring transimpedance

Calculation of circuits on transimpedance operational amplifiers

restart: with(MSpice): Devices:=[O,[TOP,AC1,2]]: Digits:=3:

ESolve(Q,`01-1_OP_TOC_Z/op-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

Calculation of circuits on transimpedance operational amplifiers

AC1 transimpedance op amp model

Kirchhoff-Laplace system

-JVF1U1-Vt1/Rt-Vt1*s*Ct

VINN = Vref

Input currents of controlled sources

JVF1U1 = I1

Solutions

{VINN, Vt1}

MSpice v8.35: pspicelib.narod.ru
Nodes given: {VINP} Sources: [Vref, VF1U1, I1]
V_NET decisions: [VOUT, VINN, Vp1, Vt1]
J_NET: [J1, JVF1U1, JRt, JCt, JFt, JVref]
Zt:=VOUT/I1, print(`On AC,`);

Zto:=Limit('Zt',s=0)=limit(Zt,s=0), print(`On direct current we get,`);

On alternating current

Zt := -Rt/(1+s*Ct*Rt)

At direct current, we get

Zto := Limit(Zt,s = 0) = -Rt

For the denominations indicated on the diagram, we get.

Values(DC,RLCVI,[]): Zt:=evalf(Zt); `Zt[f=0]`:=evalf(rhs(Zto)); #VOUT:=evalf(VOUT);

HSF([Zt],f=1..1e10,"3) semi[Zt] of transimpedance TOC op-amp);

Entering component ratings:
Rt := .10e8,10MEG"
Ct := 1/2/Pi/Ft
Ft := .10e11,10G"
DC source: DC: Vref:=0
DC source: DC: I1:=10
E1_U1 := VINP
DC source: DC: VF1U1:=0
F1_U1 := JVF1U1
E2_U1 := Vt1

Zt := -.10e8/(1.+.159e-3*s)

Zt[f=0]` := -.10e8

Calculation of circuits on transimpedance operational amplifiers

2. Transfer coefficient of a non-inverting amplifier on TOC OU

A non-inverting amplifier allows you to have a large input impedance, which allows you to have a good match with the signal source.
Rice. 4. Scheme of a non-inverting amplifier based on TOC OU

Calculation of circuits on transimpedance operational amplifiers

restart: with(MSpice): Devices:=[E,[TOP,AC2,5]]:

ESolve(Q,`OP-1_TOC_NoInvAmp/op-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

Calculation of circuits on transimpedance operational amplifiers

AC2 transimpedance op amp model

Kirchhoff-Laplace system

-Vt1/Rt-Vt1*s*Ct+(VINP-VINN)/Rn

(Vt1-VINN)/R2+(VINP-VINN)/Rn-VINN/R1

Solutions

{Vt1, VINN}

MSpice v8.35: pspicelib.narod.ru
Nodes given: {VINP} Sources: [Vinp]
V_NET decisions: [Vp1, Vt1, VOUT, VINN]
J_NET: [JR2, JR1, JRn, JRt, JRo, JCt, JFt, JVinp]

The frequency dependent gain looks like this.

H:=collect((VOUT/Vinp),s);

H := Rt*(R1+R2)/((R2*R1*Ct*Rt+Rn*R2*Ct*Rt+Rn*R1*Ct*Rt)*s+Rn*R1+R2*R1+Rt*R1+R2*Rn)

The frequency independent gain looks like this.

K:=limit(H,Ct=0);

K := Rt*(R1+R2)/(Rn*R1+R2*R1+Rt*R1+R2*Rn)

They try to reduce Ri in every possible way, equate it to n and get

K:=limit(K,Ri=0);

K := Rt*(R1+R2)/(Rn*R1+R2*R1+Rt*R1+R2*Rn)

They try to increase Rz in every possible way, let's go to infinity and get

K:=limit(K,Rt=infinity);

K := (R1+R2)/R1

Values(DC,PRN,[]):

HSF([H],f=1..1e10,"6) semiAFC of a non-inverting amplifier based on TOC OU");

Calculation of circuits on transimpedance operational amplifiers

3. Setting the bandwidth with a capacitor in the OS circuit

When using TOS OU, it is necessary to take into account its features. If in a conventional op-amp with NOS OS, when a capacitor is connected, an additional pole of the characteristic appears, then in an amplifier with TOC (Fig. 7) an additional zero and pole appear (Fig. 8).
Rice. 7. Scheme of a non-inverting amplifier based on TOC OU

Calculation of circuits on transimpedance operational amplifiers

restart: with(MSpice): Fixtures:=[O,[TOP,AC2,8]]:

ESolve(Q,`OP-1_TOC_NoInvAmp_СF/op-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

Calculation of circuits on transimpedance operational amplifiers

AC2 transimpedance op amp model

Kirchhoff-Laplace system

-Vt1/Rt-Vt1*s*Ct+(VINP-VINN)/Rn

(Vt1-VINN)*s*CF+(Vt1-VINN)/RF+(VINP-VINN)/Rn-VINN/Rg

Solutions

{VINN, Vt1}

MSpice v8.35: pspicelib.narod.ru
Nodes given: {VINP} Sources: [Vinp]
V_NET decisions: [VOUT, VINN, Vp1, Vt1]
J_NET: [JCF, JRF, JRg, JRn, JRt, JRo, JCt, JFt, JVinp]

The frequency dependent gain looks like this.

H:=collect((VOUT/Vinp),s);

H := Rt*(s*CF*RF*Rg+Rg+RF)/(Rn*s^2*CF*RF*Rg*Ct*Rt+(Rn*Rg*Ct*Rt+Rt*CF*RF* Rg+Rn*RF*Ct*Rt+RF*Rg*Ct*Rt+CF*RF*Rn*Rg)*s+Rt*Rg+Rn*Rg+RF*Rg+RF*Rn)

Zeros and poles of this function are determined by the following expressions

PoleZero(H,f);

------------- Zeros ------------

F_Zero[1] = 1/2*I*(Rg+RF)/CF/RF/Rg/Pi

----------- Poles -----------

F_Pole[1] = 1/4*I*(Rn*Rg*Ct*Rt+Rt*CF*RF*Rg+Rn*RF*Ct*Rt+RF*Rg*Ct*Rt+CF*RF*Rn*Rg-(-2*Rn*Rg^2*Ct*Rt^2*CF*RF+2*Rn^2*Rg*Ct^2*Rt^2*RF+2*Rn*Rg^2*Ct^2*Rt^2*RF-2*Rn^2*Rg^2*Ct*Rt*CF*RF+2*Rt^2*CF*RF^2*Rg*Rn*Ct+2*...

F_Pole[2] = 1/4*I*(Rn*Rg*Ct*Rt+Rt*CF*RF*Rg+Rn*RF*Ct*Rt+RF*Rg*Ct*Rt+CF*RF*Rn*Rg+(-2*Rn*Rg^2*Ct*Rt^2*CF*RF+2*Rn^2*Rg*Ct^2*Rt^2*RF+2*Rn*Rg^2*Ct^2*Rt^2*RF-2*Rn^2*Rg^2*Ct*Rt*CF*RF+2*Rt^2*CF*RF^2*Rg*Rn*Ct+2*...

They try to reduce Ct to zero, and they try to increase Rt in every possible way.

Let's let Ct go to zero and Rt to infinity, and we get

H_ideal:=limit(subs(Ct=0,H),Rt=infinity);

H_ideal := (s*CF*RF*Rg+Rg+RF)/Rg/(s*CF*RF+1)

The frequency independent gain looks like this.

K:=limit(H,s=0);

K := Rt*(Rg+RF)/(Rt*Rg+Rn*Rg+RF*Rg+Rn*RF)

Rt is tried in every possible way to reduce, equate it to infinity and get

K_ideal:=limit(K,Rt=infinity);

K_ideal := (Rg+RF)/Rg

Values(DC,RLVCI,[]):

Entering component ratings:
CF := .1000e-8,1000p"
RF := .1e4,1K"
Rg := .1e4,1K"
Rn := 25,25"
Rt := .10e8,10MEG"
Ro := 75,75"
Ct := 1/2/Pi/Ft
Ft := .10e11,10G"
DC source: DC: Vinp:=0
E1_U1 := VINP
H1_U1 := (Vp1-VINN)/Rn
E2_U1 := Vt1
HSF([H,H_ideal],f=1..1e7,"9) semi[H,H_ideal] of a non-inverting TOC op amp");

Calculation of circuits on transimpedance operational amplifiers

4. 1 MHz band pass filter with TOC op amp

Previously, it was considered uneconomical to implement active filters at frequencies above 1 MHz.

Currently, the problem is being solved head-on, using the TOS OU.

Application of the model (Fig. 11) makes it possible to obtain an upper estimate of the CO non-ideality indicators,

under which the required filter can be implemented.
Rice. 10. Scheme of a non-inverting amplifier based on TOC OU

Calculation of circuits on transimpedance operational amplifiers

restart: with(MSpice): Devices:=[O,[TOP,AC4,11]]:

ESolve(Q,`04-1_TOC_Filter/op-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

Calculation of circuits on transimpedance operational amplifiers

AC4 transimpedance op amp model

Kirchhoff-Laplace system

(VOUT-V4)/RF+(V2-V4)/Rn-V4/Rg

-VOUT/Ro-Vt1/Ro-VOUT*s*Co-(VOUT-V4)/RF-(VOUT-V1)/R3

-V2/R2-V2/Rd-V2*s*Cd-(V2-V1)*s*C2

(V2-V1)*s*C2+(VOUT-V1)/R3-(V1-Vinp)/R1-V1*s*C1

-Vt1/Rt-(V2-V4)/Rn-Vt1*s*Ct

Solutions

{VOUT, V1, V2, V4, Vt1}

MSpice v8.35: pspicelib.narod.ru
Nodes given: {VINP} Sources: [Vinp]
V_NET Solutions: [VOUT, V1, V2, V4, Vp1, Vt1]
J_NET: [JVinp, JRF, JR1, JC2, JRg, JR2, JC1, JRd, JRn, JRt, JRo, JCt, JFt, JCo, JCd, JR3]

If the conditions for ifilter are satisfied

R1:=Rg: R2:=Rg: R3:=Rg: C1:=C2:

Then the frequency dependent gain will look like this.

H:=simplify(VOUT/Vinp,'size');

H := (s*C2*Rd*(Ro*Ct*Rt*s+Ro+Rt)*Rg^3+(Rd*Ro*Ct*Rt*(C2+Cd)*(Rn+RF)*s^2+(((C2+Cd)*(Rn+RF)*Ro+C2*Rt*RF)*Rd+Ro*Ct*Rt*(Rn+RF))*s+Ro*(Rn+RF))*Rg^2+Ro*(RF*Rn*Rd*(C2+Cd)*s+(Rn+RF)*Rd+RF*Rn)*(Ct*Rt*s+1)*Rg+RF*...

Center frequency and frequency response graph (Fig. 12).

Values(AC,RLCVI,[]): H:=evalf(H,2);

HSF([H],f=1e5..1e7,"12) semiAFC$200 of a non-inverting amplifier based on TOS op-amp");

Entering component ratings:
R1 := 300,300"
C2 := .750e-9,750p"
RF := .1e4,1K"
R3 := 300,300"
Rg := 300,300"
R2 := 300,300"
C1 := .750e-9,750p"
Rd := .1e7,1MEG"
Rn := 25,25"
Rt := .10e8,10MEG"
Ro := 75,75"
Ct := 1/2/Pi/Ft
Ft := .10e11,10G"
Co := .5e-11,5p"
CD := .3e-11,3p"
AC source: DC: Vinp:=0 AC: Vinp:=1 Pfase(degrees):=0
E1_U1 := V2
H1_U1 := (Vp1-V4)/Rn
H2_U1 := Vt1/Ro

H := (.20e5*s*(.12e-1*s+.10e8)+.80e3*s^2+.68e12*s+.19e13+.22e5*(19.*s+.10e10)*(.16e-3*s+1.))/(12.*s*(1.+.38e-3*s)*(.61e-10*s^2+.17*s+.10e8)+.24e-13*s^4+.26e-3*s^3+.18e5*s^2-.6e11*s+.18e19+.30e3*(.42e4*...

Calculation of circuits on transimpedance operational amplifiers

Literature

Petrakov. O. M. Analytical calculations in electronics Magazine SCHEMOTEHNIKA, No. 7, 2006.
Dyakonov V.P. Maple-9 in mathematics, physics, education. M.: SOLON-Press, 2004.
V. D. RAZEVIG OrCAD design system 9.2. SOLON. Moscow 2001
Razevig V. D. Circuit modeling using Micro-Cap 7. - M .: Hot line-Telecom, 2003.
Behavioral modeling in PSPICE. Circuitry No. 3, No. 4, for 2003
Petrakov OM Creation of analog PSPICE-models of radioelements. RADIOSOFT", 2004
pspice.narod.ru Electronic CAD. Modeling. Circuitry.
Razevig VD Simulation of analog electronic devices on personal computers. MPEI Publishing House, 1993
Heineman R. PSpice simulation of electronic circuits. DMK Press, 2002

Publication: cxem.net

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