dsd11-12 / dsd-11=ТКС / dsd-11=ТКС / Kulakov

Общий коэффициент преобразования смесителя G’c*A с синусоидальным сигналом гетеродина оказывается выше (π/4), чем коэффициент преобразования смесителя с прямоугольным сигналом гетеродина (2/π).

В случае, если выключение ключей одного пути протекания тока происходит до момента включения ключей другого пути (рис.5 в), общий коэффициент преобразования смесителя описывается выражением:

При r→1, AG’c также стремится к 1, однако линейность смесителя в этом случае резко падает. Коэффициент шума смесителя коммутируемого напряжением описывается выражением

F= Lc 1+ 2Rm

Rs

где Lc- потеря мощности при преобразовании сигнала, Rs- сопротивление источника сигнала, Rm- среднее значение сопротивления ключа за период сигнала гетеродина.

Лекция 8.

Возможности программы SpectreRF для расчета радиочастотных схем

Материал данной лекции полностью основан на описании данной программы, приведенной ф.Cadence в документах “Affirma RF Simulator (SpectreRF) Theory” и “Affirma RF Simulator User Guide”.

Поэтому заинтересованным слушателям настоятельно рекомендуется обратится к оригиналам. Ниже приводятся цитаты из данных описаний, которые позволят составить общее представление о возможности программы.

“SpectreRF simulation is an option to the Spectre circuit simulator that adds capabilities to spectre that are particularly useful to analog and RF designers, including the ability to

*Efficiently and directly compute a steady-state solution *Characterize circuits that translate frequency”

“SpectreRF simulation brings several concepts to the Spectre simulator.

*Periodic Steady-State analysis—PSS

*Periodic Small-Signal analyses—PAC, PSP, PXF, and Pnoise

*Periodic Distortion analysis—Pdisto

*Quasi-Periodic Noise analysis—QPnoise

*Envelope Following analysis”

“Periodic Steady-State (PSS)analysis is a large-signal analysis that directly computes the periodic steadystate response of a circuit with a simulation time that is independent of the time constants of the circuit. PSS quickly computes the steady-state response of circuits that exhibit extremely long time constants, such as high-Q filters and oscillators.”

“Periodic Small-Signal (PAC, PSP, PXF, and Pnoise) analyses are similar to the conventional smallsignal analyses (AC, SP, XF, and Noise) but you can apply them to periodic circuits where frequency conversion plays a critical role. The conventional smallsignal analyses (AC, SP, XF, and Noise) linearize about the DC or time-invariant operating point and they do not include frequency conversion effects. Once the simulator has performed a PSS analysis, it can linearize the circuit about a periodic (time varying) operating point and can include frequency conversion effects. After performing a PSS analysis, you can perform one or more of the periodic small-signal analyses. Example circuits where you might use the Periodic small-signal analyses include conversion gain in mixers, noise in oscillators, and switched-capacitor filters.”

“Periodic Distortion (Pdisto) analysis is another large signal analysis you can use for circuits with multiple large tones. Pdisto analysis computes the steady-state responses of a circuit driven by two or more signals at unrelated frequencies. You select one sinusoidal or pulse signal as the large signal. Any additional signals, called moderate signals, must be sinusoids. This analysis is also called Quasi-Periodic Steady-State (QPSS) analysis.”

“Quasi-Periodic Noise (QPnoise) analysis is similar to the Pnoise analysis, except that it includes frequency conversion and intermodulation effects. QPnoise analysis is useful for predicting the noise behavior of mixers, switched-capacitor filters and other periodically or quasi-periodically driven circuits. QPnoise analysis linearizes the circuit about the quasiperiodic

operating point computed in the prerequisite Pdisto analysis. It is the quasiperiodically time-varying nature of the linearized circuit that accounts for the frequency conversion and intermodulation.”

“Envelope Following analysis allows RF circuit designers to efficiently and accurately predict the envelope transient response of the RF circuits used in communication systems.”

“PSS analysis does not support distributed components or components with hidden state. The difficulty with distributed components results from the fact that the state of a distributed component is a waveform, not a simple number, as with capacitors and inductors. To know the state of a distributed component, it is necessary to know the voltage and current along the whole length of the component. The Transmission Line Modeler, which is available with SpectreRF, generates transmission line models which you can use in SpectreRF simulations.”

“There are two fundamental assumptions that apply to PSS analysis

*Periodicity

*Linearity”

“PSS analysis assumes that during the shooting interval, all stimuli are periodic and that the circuit supports a T-periodic response, where Tis the period specified to the PSS analysis. If the circuit is driven with more than one periodic stimulus, then the frequencies must all be commensurate or co-periodic, and Tmust be the common period or some integer multiple of

it. Efficiency of the simulation drops when the Tis long compared to the periods of the stimuli. If the circuit is driven by T-periodic stimuli but does not have a T-periodic solution (for example, if the solution is chaotic), PSS analysis fails to converge. In this case, you should use transient analysis to simulate the circuit. Occasionally a circuit generates subharmonics, as is the case with frequency dividers. In this situation, you should specify the PSS period to be equal to that of the subharmonics.”

“In the circuit under simulation, the relationship between the initial and final points over the shooting interval should be near-linear. The more nonlinear the relationship between initial and final points, the greater number of iterations needed by the PSS analysis, which causes the PSS analysis to take longer. If the relationship is sufficiently nonlinear, PSS analysis might

not converge.”

“Circuits designed to translate from one frequency to another include

*mixers

*detectors

*samplers

*frequency multipliers

*phase-locked loops

*parametric oscillators

Such circuits are commonly found in wireless communication systems.”

“You cannot simulate any of the circuits listed in the previous paragraphs with conventional small-signal analyses because they exhibit a nonnegligible amount of frequency translation. SpectreRF simulation provides the periodic small-signal analyses: PAC, PSP, PXF, and Pnoise [telichevesky96b]. These analyses start by linearizing the circuit about the periodically time-varying operating point computed by a preceding PSS analysis.”

“Applying a periodic small-signal analysis is a two-step process.

*First, the small input or noise signals are ignored and PSS analysis is used to compute the periodic steady-state response to the remaining large signals (such as the clock orthe LO). During the course of the PSS analysis, the circuit is linearized about the periodic largesignal operating point.

Then the subsequent periodic small-signal analyses use this periodic operating point to predict the response of the circuit to a small sinusoid at an arbitrary frequency. Once you know the periodic large-signal operating point, you can perform any number of periodic small-signal analyses.”

“There are two fundamental assumptions that apply to the periodic small-signal analyses

*Linearity

*Frequency”

“The periodic small-signal analyses all assume that the circuit responds linearly to the sinusoidal (PAC or PXF) or noise (PNoise) stimulus, or it involves both sinusoidal and noise (PSP) stimuli. There is no such assumption concerning the periodic signals (such as the LO or clock) applied in the initial PSS analysis. SpectreRF simulation is not capable of computing the distortion caused by the small signals, although you can use the small signals to measure distortion caused by the large signals present in the PSS analysis. Internally, the periodic small-signal analyses compute transfer functions using time domain techniques. The time-steps used in these time-domain computations are the same as those used in the preceding PSS analysis. In order for the transfer function to be accurate, the period of the small sinusoidal stimulus must be large compared with the largest timestep used during the PSS analysis.”

“If the analysis frequency of the periodic small-signal analysis is too high, the accuracy of the results degrade. The Spectre simulator warns you when it determines that you are requesting a frequency that is too high. You can use the maxacfreq parameter of the PSS analysis to specify the highest frequency that SpectreRF simulation can use in subsequent periodic” small-signal analyses. PSS analysis then chooses the time-step in order to assure the results computed by the small-signal analyses are accurate. Specifying a very large maxacfreq causes both the PSS and small-signal analyses to run slowly and requires a large amount of memory.”

“The Periodic Distortion (Pdisto) analysis lets you calculate the response due to multiple input frequencies. All of the input signals are treated in the same way as the PSS drive source, so that the calculated output includes all the intermodulation distortion effects caused by frequency translation of all harmonics of the input signals. You can analyze the response of a circuit to a sum of signal sinusoids with PSS analysis by including them as components of the PSS drive source, but the resulting sum must be periodic. Choose Pdisto analysis when you need to compute the steady-state responses of a circuit

driven by two or more signals at unrelated frequencies. Unlike PSS analysis, Pdisto analysis does not require that multiple periodic stimuli be coperiodic. When you use Pdisto analysis, you declare one signal as large. That signal can be a sinusoid or a pulse. Any additionalsignals, called moderate signals, must be sinusoids. You must specify the number of harmonics to be simulated on all moderate tones.”

“The Quasi-Periodic Noise (QPnoise) analysis is similar to the conventional Pnoise analysis, except that, in addition, it includes frequency conversion and intermodulation effects. You can use QPnoise analysis to predict the noise behavior of mixers, switched-capacitor filters, and other periodically or quasi-periodically driven circuits. QPnoise analysis linearizes the circuit about the quasi-periodic operating point computed in the prerequisite Pdisto analysis. It is the quasi-periodically time-varying nature of the linearized circuit that accounts for the frequency conversion and intermodulation.”

“Envelope following analysis allows RF circuit designers to efficiently and accurately predict the envelope transient response of the RF circuits used in communication systems. For example, it allows an RF designer to predict the spectral regrowth of a mixer.”

Лекция 8.

Расчет узкополосных малошумящих РЧ КМОП усилителей

Индуктивное вырождение истока входного МОП транзистора малошумящего усилительного каскада используется с целью модификации входного импеданса каскада, которая приводит к появлению чисто резистивной составляющей. Резистивная составляющая используется для согласования входного сопротивления усилителя и сопротивления источника сигнала на резонансной частоте. При этом важно отметить, что получаемая резистивная составляющая не вносит дополнительных шумов.

Входная часть каскада с индуктивным вырождением показана на рис.1., а ее эквивалентная схема приведена на рис.2. Анализ эквивалентной схемы приводит к следующему выражению для входного импеданса каскада:

Входной импеданс содержит чисто резистивную составляющую gm(Ls/Cgs), которая на резонансной частоте последовательного колебательного контура (Ls - Cgs)

может быть использована для согласования входного сопротивления каскада и источника. Однако одновременное выполнение требований по входному сопротивлению и частоте

резонанса приводит к неоптимальному выбору размеров транзистора и его режима работы. Для того, чтобы оптимизировать входную часть каскада, в цепь затвора транзистора вводят дополнительную индуктивность Lg. В этом случае возможна относительно независимая настройка резонансной частоты усилителя и его входного сопротивления. Резонансная частота в данном случае расчитывается по формуле

fr = 2π (Ls 1+ Lg )Cgs ,

в то время как резистивная составляющая описывается тем же выражением -gm(Ls/Cgs). Оптимальное с точки зрения шумов согласование требует выполнения соотношения

где QLopt – оптимальная добротность входного контура, образованного входными цепями усилителя и источника сигнала,

p = δα2

5γ .

В этом случае оптимальный коэффициент шума каскада описывается выражением:

С учетом всего вышеизложенного, процедура расчета входных цепей малошумящего узкополосного усилителя состоит из следующих шагов:

1.Выбрать наименьшую технологически хорошо контроллируемую индуктивность Ls (1-3 нГн).

2. Выбрать частоту единичного усиления трензистора, исходя из выражения

LsωT = gm Ls = Rs . Cgs

3.Зная значения параметров транзисторов α, δ и γ определить параметр p и оптимальную добротность QLopt.

4.Зная рабочую частоту каскада ω0 найти номинал индуктивности затвора

5.Определить емкость затвор-исток транзистора, используя выражение

6.Учитывая, что Cgs = (2 / 3)CoxWL определить W, считая длину канала транзистора минимальной.

7.Определить gm = ωT Cgs .

g L

8.Определить =VGS −VT μnCoxW .

9.Определить режим транзистора по току ID = (1/ 2)gmVeff .Vref = m